Characteristic Classes Am 76 Volume 76

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Characteristic Classes. (AM-76), Volume 76

John Milnor,James D. Stasheff
Characteristic Classes AM 76 Volume 76 Book PDF

Author : John Milnor,James D. Stasheff
Publisher : Princeton University Press
Page : 340 pages
File Size : 55,6 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400881826

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Characteristic Classes. (AM-76), Volume 76 by John Milnor,James D. Stasheff Pdf

The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory. As such, it is a fundamental and an essential tool in the study of differentiable manifolds. In this volume, the authors provide a thorough introduction to characteristic classes, with detailed studies of Stiefel-Whitney classes, Chern classes, Pontrjagin classes, and the Euler class. Three appendices cover the basics of cohomology theory and the differential forms approach to characteristic classes, and provide an account of Bernoulli numbers. Based on lecture notes of John Milnor, which first appeared at Princeton University in 1957 and have been widely studied by graduate students of topology ever since, this published version has been completely revised and corrected.

Current Trends in Analysis, its Applications and Computation

Paula Cerejeiras,Michael Reissig,Irene Sabadini,Joachim Toft
Current Trends in Analysis its Applications and Computation Book PDF

Author : Paula Cerejeiras,Michael Reissig,Irene Sabadini,Joachim Toft
Publisher : Springer Nature
Page : 663 pages
File Size : 53,7 Mb
Release : 2022-10-03
Category : Mathematics
ISBN : 9783030875022

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Current Trends in Analysis, its Applications and Computation by Paula Cerejeiras,Michael Reissig,Irene Sabadini,Joachim Toft Pdf

This volume contains the contributions of the participants of the 12th ISAAC congress which was held at the University of Aveiro, Portugal, from July 29 to August 3, 2019. These contributions originate from the following sessions: Applications of dynamical systems theory in biology, Complex Analysis and Partial Differential Equations, Complex Geometry, Complex Variables and Potential Theory, Constructive Methods in the Theory of Composite and Porous Media, Function Spaces and Applications, Generalized Functions and Applications, Geometric & Regularity Properties of Solutions to Elliptic and Parabolic PDEs, Geometries Defined by Differential Forms, Partial Differential Equations on Curved Spacetimes, Partial Differential Equations with Nonstandard Growth, Quaternionic and Clifford Analysis, Recent Progress in Evolution Equations, Wavelet theory and its Related Topics.

Equivariant Ordinary Homology and Cohomology

Steven R. Costenoble,Stefan Waner
Equivariant Ordinary Homology and Cohomology Book PDF

Author : Steven R. Costenoble,Stefan Waner
Publisher : Springer
Page : 294 pages
File Size : 49,6 Mb
Release : 2017-01-02
Category : Mathematics
ISBN : 9783319504483

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Equivariant Ordinary Homology and Cohomology by Steven R. Costenoble,Stefan Waner Pdf

Filling a gap in the literature, this book takes the reader to the frontiers of equivariant topology, the study of objects with specified symmetries. The discussion is motivated by reference to a list of instructive “toy” examples and calculations in what is a relatively unexplored field. The authors also provide a reading path for the first-time reader less interested in working through sophisticated machinery but still desiring a rigorous understanding of the main concepts. The subject’s classical counterparts, ordinary homology and cohomology, dating back to the work of Henri Poincaré in topology, are calculational and theoretical tools which are important in many parts of mathematics and theoretical physics, particularly in the study of manifolds. Similarly powerful tools have been lacking, however, in the context of equivariant topology. Aimed at advanced graduate students and researchers in algebraic topology and related fields, the book assumes knowledge of basic algebraic topology and group actions.

The Geometric Hopf Invariant and Surgery Theory

Michael Crabb,Andrew Ranicki
The Geometric Hopf Invariant and Surgery Theory Book PDF

Author : Michael Crabb,Andrew Ranicki
Publisher : Springer
Page : 397 pages
File Size : 42,6 Mb
Release : 2018-01-24
Category : Mathematics
ISBN : 9783319713069

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The Geometric Hopf Invariant and Surgery Theory by Michael Crabb,Andrew Ranicki Pdf

Written by leading experts in the field, this monograph provides homotopy theoretic foundations for surgery theory on higher-dimensional manifolds. Presenting classical ideas in a modern framework, the authors carefully highlight how their results relate to (and generalize) existing results in the literature. The central result of the book expresses algebraic surgery theory in terms of the geometric Hopf invariant, a construction in stable homotopy theory which captures the double points of immersions. Many illustrative examples and applications of the abstract results are included in the book, making it of wide interest to topologists. Serving as a valuable reference, this work is aimed at graduate students and researchers interested in understanding how the algebraic and geometric topology fit together in the surgery theory of manifolds. It is the only book providing such a wide-ranging historical approach to the Hopf invariant, double points and surgery theory, with many results old and new.

Stein Manifolds and Holomorphic Mappings

Franc Forstnerič
Stein Manifolds and Holomorphic Mappings Book PDF

Author : Franc Forstnerič
Publisher : Springer
Page : 569 pages
File Size : 42,6 Mb
Release : 2017-09-05
Category : Mathematics
ISBN : 9783319610580

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Stein Manifolds and Holomorphic Mappings by Franc Forstnerič Pdf

This book, now in a carefully revised second edition, provides an up-to-date account of Oka theory, including the classical Oka-Grauert theory and the wide array of applications to the geometry of Stein manifolds. Oka theory is the field of complex analysis dealing with global problems on Stein manifolds which admit analytic solutions in the absence of topological obstructions. The exposition in the present volume focuses on the notion of an Oka manifold introduced by the author in 2009. It explores connections with elliptic complex geometry initiated by Gromov in 1989, with the Andersén-Lempert theory of holomorphic automorphisms of complex Euclidean spaces and of Stein manifolds with the density property, and with topological methods such as homotopy theory and the Seiberg-Witten theory. Researchers and graduate students interested in the homotopy principle in complex analysis will find this book particularly useful. It is currently the only work that offers a comprehensive introduction to both the Oka theory and the theory of holomorphic automorphisms of complex Euclidean spaces and of other complex manifolds with large automorphism groups.

An Invitation to Modern Enumerative Geometry

Andrea T. Ricolfi
An Invitation to Modern Enumerative Geometry Book PDF

Author : Andrea T. Ricolfi
Publisher : Springer Nature
Page : 310 pages
File Size : 41,8 Mb
Release : 2022-12-14
Category : Mathematics
ISBN : 9783031114991

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An Invitation to Modern Enumerative Geometry by Andrea T. Ricolfi Pdf

This book is based on a series of lectures given by the author at SISSA, Trieste, within the PhD courses Techniques in enumerative geometry (2019) and Localisation in enumerative geometry (2021). The goal of this book is to provide a gentle introduction, aimed mainly at graduate students, to the fast-growing subject of enumerative geometry and, more specifically, counting invariants in algebraic geometry. In addition to the more advanced techniques explained and applied in full detail to concrete calculations, the book contains the proofs of several background results, important for the foundations of the theory. In this respect, this text is conceived for PhD students or research “beginners” in the field of enumerative geometry or related areas. This book can be read as an introduction to Hilbert schemes and Quot schemes on 3-folds but also as an introduction to localisation formulae in enumerative geometry. It is meant to be accessible without a strong background in algebraic geometry; however, three appendices (one on deformation theory, one on intersection theory, one on virtual fundamental classes) are meant to help the reader dive deeper into the main material of the book and to make the text itself as self-contained as possible.

Surveys on Surgery Theory (AM-145), Volume 1

Sylvain Cappell,Andrew Ranicki,Jonathan Rosenberg
Surveys on Surgery Theory AM 145 Volume 1 Book PDF

Author : Sylvain Cappell,Andrew Ranicki,Jonathan Rosenberg
Publisher : Princeton University Press
Page : 448 pages
File Size : 46,9 Mb
Release : 2014-09-08
Category : Mathematics
ISBN : 9781400865192

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Surveys on Surgery Theory (AM-145), Volume 1 by Sylvain Cappell,Andrew Ranicki,Jonathan Rosenberg Pdf

Surgery theory, the basis for the classification theory of manifolds, is now about forty years old. There have been some extraordinary accomplishments in that time, which have led to enormously varied interactions with algebra, analysis, and geometry. Workers in many of these areas have often lamented the lack of a single source that surveys surgery theory and its applications. Indeed, no one person could write such a survey. The sixtieth birthday of C. T. C. Wall, one of the leaders of the founding generation of surgery theory, provided an opportunity to rectify the situation and produce a comprehensive book on the subject. Experts have written state-of-the-art reports that will be of broad interest to all those interested in topology, not only graduate students and mathematicians, but mathematical physicists as well. Contributors include J. Milnor, S. Novikov, W. Browder, T. Lance, E. Brown, M. Kreck, J. Klein, M. Davis, J. Davis, I. Hambleton, L. Taylor, C. Stark, E. Pedersen, W. Mio, J. Levine, K. Orr, J. Roe, J. Milgram, and C. Thomas.

Foundations of Mathematics and Physics One Century After Hilbert

Joseph Kouneiher
Foundations of Mathematics and Physics One Century After Hilbert Book PDF

Author : Joseph Kouneiher
Publisher : Springer
Page : 441 pages
File Size : 53,5 Mb
Release : 2018-05-26
Category : Science
ISBN : 9783319648132

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Foundations of Mathematics and Physics One Century After Hilbert by Joseph Kouneiher Pdf

This book explores the rich and deep interplay between mathematics and physics one century after David Hilbert’s works from 1891 to 1933, published by Springer in six volumes. The most prominent scientists in various domains of these disciplines contribute to this volume providing insight to their works, and analyzing the impact of the breakthrough and the perspectives of their own contributions. The result is a broad journey through the most recent developments in mathematical physics, such as string theory, quantum gravity, noncommutative geometry, twistor theory, Gauge and Quantum fields theories, just to mention a few. The reader, accompanied on this journey by some of the fathers of these theories, explores some far reaching interfaces where mathematics and theoretical physics interact profoundly and gets a broad and deep understanding of subjects which are at the core of recent developments in mathematical physics. The journey is not confined to the present state of the art, but sheds light on future developments of the field, highlighting a list of open problems. Graduate students and researchers working in physics, mathematics and mathematical physics will find this journey extremely fascinating. All those who want to benefit from a comprehensive description of all the latest advances in mathematics and mathematical physics, will find this book very useful too.

Nilpotence and Periodicity in Stable Homotopy Theory. (AM-128), Volume 128

Douglas C. Ravenel
Nilpotence and Periodicity in Stable Homotopy Theory AM 128 Volume 128 Book PDF

Author : Douglas C. Ravenel
Publisher : Princeton University Press
Page : 224 pages
File Size : 43,5 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882489

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Nilpotence and Periodicity in Stable Homotopy Theory. (AM-128), Volume 128 by Douglas C. Ravenel Pdf

Nilpotence and Periodicity in Stable Homotopy Theory describes some major advances made in algebraic topology in recent years, centering on the nilpotence and periodicity theorems, which were conjectured by the author in 1977 and proved by Devinatz, Hopkins, and Smith in 1985. During the last ten years a number of significant advances have been made in homotopy theory, and this book fills a real need for an up-to-date text on that topic. Ravenel's first few chapters are written with a general mathematical audience in mind. They survey both the ideas that lead up to the theorems and their applications to homotopy theory. The book begins with some elementary concepts of homotopy theory that are needed to state the problem. This includes such notions as homotopy, homotopy equivalence, CW-complex, and suspension. Next the machinery of complex cobordism, Morava K-theory, and formal group laws in characteristic p are introduced. The latter portion of the book provides specialists with a coherent and rigorous account of the proofs. It includes hitherto unpublished material on the smash product and chromatic convergence theorems and on modular representations of the symmetric group.

Characteristic Classes

John Willard Milnor,James D. Stasheff
Characteristic Classes Book PDF

Author : John Willard Milnor,James D. Stasheff
Publisher : Princeton University Press
Page : 342 pages
File Size : 46,6 Mb
Release : 1974
Category : Mathematics
ISBN : 0691081220

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Characteristic Classes by John Willard Milnor,James D. Stasheff Pdf

The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory. As such, it is a fundamental and an essential tool in the study of differentiable manifolds. In this volume, the authors provide a thorough introduction to characteristic classes, with detailed studies of Stiefel-Whitney classes, Chern classes, Pontrjagin classes, and the Euler class. Three appendices cover the basics of cohomology theory and the differential forms approach to characteristic classes, and provide an account of Bernoulli numbers. Based on lecture notes of John Milnor, which first appeared at Princeton University in 1957 and have been widely studied by graduate students of topology ever since, this published version has been completely revised and corrected.

Index Theory and Operator Algebras

Jeffrey Stephen Fox,Peter Haskell
Index Theory and Operator Algebras Book PDF

Author : Jeffrey Stephen Fox,Peter Haskell
Publisher : American Mathematical Soc.
Page : 190 pages
File Size : 49,9 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821851524

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Index Theory and Operator Algebras by Jeffrey Stephen Fox,Peter Haskell Pdf

This collection of papers by leading researchers provides a broad picture of current research directions in index theory. Based on lectures presented at the NSF-CBMS Regional Conference on K-Homology and Index Theory, held in August 1991 at the University of Colorado at Boulder, the book provides both a careful exposition of new perspectives in classical index theory and an introduction to currently active areas of the field. Presented here are two new proofs of the classical Atiyah-Singer Index Theorem, as well as index theorems for manifolds with boundary and open manifolds. Index theory for semi-simple p-adic groups and the geometry of discrete groups are also discussed. Through-out the book, the application of operator algebras emerges as a central theme. Aimed at graduate students and researchers, this book would be suitable as a text for an advanced graduate topics course on index theory.

Surveys on Surgery Theory (AM-149), Volume 2

Sylvain Cappell,Andrew Ranicki,Jonathan Rosenberg
Surveys on Surgery Theory AM 149 Volume 2 Book PDF

Author : Sylvain Cappell,Andrew Ranicki,Jonathan Rosenberg
Publisher : Princeton University Press
Page : 446 pages
File Size : 47,8 Mb
Release : 2014-09-08
Category : Mathematics
ISBN : 9781400865215

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Surveys on Surgery Theory (AM-149), Volume 2 by Sylvain Cappell,Andrew Ranicki,Jonathan Rosenberg Pdf

Surgery theory, the basis for the classification theory of manifolds, is now about forty years old. The sixtieth birthday (on December 14, 1996) of C.T.C. Wall, a leading member of the subject's founding generation, led the editors of this volume to reflect on the extraordinary accomplishments of surgery theory as well as its current enormously varied interactions with algebra, analysis, and geometry. Workers in many of these areas have often lamented the lack of a single source surveying surgery theory and its applications. Because no one person could write such a survey, the editors asked a variety of experts to report on the areas of current interest. This is the second of two volumes resulting from that collective effort. It will be useful to topologists, to other interested researchers, and to advanced students. The topics covered include current applications of surgery, Wall's finiteness obstruction, algebraic surgery, automorphisms and embeddings of manifolds, surgery theoretic methods for the study of group actions and stratified spaces, metrics of positive scalar curvature, and surgery in dimension four. In addition to the editors, the contributors are S. Ferry, M. Weiss, B. Williams, T. Goodwillie, J. Klein, S. Weinberger, B. Hughes, S. Stolz, R. Kirby, L. Taylor, and F. Quinn.

4-Manifolds

Selman Akbulut
4 Manifolds Book PDF

Author : Selman Akbulut
Publisher : Oxford University Press
Page : 280 pages
File Size : 44,6 Mb
Release : 2016-09-08
Category : Mathematics
ISBN : 9780191087752

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4-Manifolds by Selman Akbulut Pdf

This book presents the topology of smooth 4-manifolds in an intuitive self-contained way, developed over a number of years by Professor Akbulut. The text is aimed at graduate students and focuses on the teaching and learning of the subject, giving a direct approach to constructions and theorems which are supplemented by exercises to help the reader work through the details not covered in the proofs. The book contains a hundred colour illustrations to demonstrate the ideas rather than providing long-winded and potentially unclear explanations. Key results have been selected that relate to the material discussed and the author has provided examples of how to analyse them with the techniques developed in earlier chapters.

Geometrodynamics of Gauge Fields

Eckehard W. Mielke
Geometrodynamics of Gauge Fields Book PDF

Author : Eckehard W. Mielke
Publisher : Springer
Page : 377 pages
File Size : 51,8 Mb
Release : 2017-01-22
Category : Science
ISBN : 9783319297347

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Geometrodynamics of Gauge Fields by Eckehard W. Mielke Pdf

This monograph aims to provide a unified, geometrical foundation of gauge theories of elementary particle physics. The underlying geometrical structure is unfolded in a coordinate-free manner via the modern mathematical notions of fibre bundles and exterior forms. Topics such as the dynamics of Yang-Mills theories, instanton solutions and topological invariants are included. By transferring these concepts to local space-time symmetries, generalizations of Einstein's theory of gravity arise in a Riemann-Cartan space with curvature and torsion. It provides the framework in which the (broken) Poincaré gauge theory, the Rainich geometrization of the Einstein-Maxwell system, and higher-dimensional, non-abelian Kaluza-Klein theories are developed. Since the discovery of the Higgs boson, concepts of spontaneous symmetry breaking in gravity have come again into focus, and, in this revised edition, these will be exposed in geometric terms. Quantizing gravity remains an open issue: formulating it as a de Sitter type gauge theory in the spirit of Yang-Mills, some new progress in its topological form is presented. After symmetry breaking, Einstein’s standard general relativity with cosmological constant emerges as a classical background. The geometrical structure of BRST quantization with non-propagating topological ghosts is developed in some detail.

Homology Theory

James W. Vick
Homology Theory Book PDF

Author : James W. Vick
Publisher : Springer Science & Business Media
Page : 258 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461208815

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Homology Theory by James W. Vick Pdf

This introduction to some basic ideas in algebraic topology is devoted to the foundations and applications of homology theory. After the essentials of singular homology and some important applications are given, successive topics covered include attaching spaces, finite CW complexes, cohomology products, manifolds, Poincare duality, and fixed point theory. This second edition includes a chapter on covering spaces and many new exercises.