Homotopy Theory Of Function Spaces And Related Topics

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Homotopy Theory of Function Spaces and Related Topics

Yves Félix,Gregory Lupton,Samuel B. Smith
Homotopy Theory of Function Spaces and Related Topics Book PDF

Author : Yves Félix,Gregory Lupton,Samuel B. Smith
Publisher : American Mathematical Soc.
Page : 246 pages
File Size : 45,8 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821849293

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Homotopy Theory of Function Spaces and Related Topics by Yves Félix,Gregory Lupton,Samuel B. Smith Pdf

This volume contains the proceedings of the Workshop on Homotopy Theory of Function Spaces and Related Topics, which was held at the Mathematisches Forschungsinstitut Oberwolfach, in Germany, from April 5-11, 2009. This volume contains fourteen original research articles covering a broad range of topics that include: localization and rational homotopy theory, evaluation subgroups, free loop spaces, Whitehead products, spaces of algebraic maps, gauge groups, loop groups, operads, and string topology. In addition to reporting on various topics in the area, this volume is supposed to facilitate the exchange of ideas within Homotopy Theory of Function Spaces, and promote cross-fertilization between Homotopy Theory of Function Spaces and other areas. With these latter aims in mind, this volume includes a survey article which, with its extensive bibliography, should help bring researchers and graduate students up to speed on activity in this field as well as a problems list, which is an expanded and edited version of problems discussed in sessions held at the conference. The problems list is intended to suggest directions for future work.

Function Spaces in Modern Analysis

Krzysztof Jarosz
Function Spaces in Modern Analysis Book PDF

Author : Krzysztof Jarosz
Publisher : American Mathematical Soc.
Page : 256 pages
File Size : 40,7 Mb
Release : 2011-07-18
Category : Mathematics
ISBN : 9780821852514

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Function Spaces in Modern Analysis by Krzysztof Jarosz Pdf

This volume contains the proceedings of the Sixth Conference on Function Spaces, which was held from May 18-22, 2010, at Southern Illinois University at Edwardsville. The papers cover a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), spaces of integrable functions, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and other related subjects.

Lie Models in Topology

Urtzi Buijs,Yves Félix,Aniceto Murillo,Daniel Tanré
Lie Models in Topology Book PDF

Author : Urtzi Buijs,Yves Félix,Aniceto Murillo,Daniel Tanré
Publisher : Springer Nature
Page : 283 pages
File Size : 49,6 Mb
Release : 2020-12-15
Category : Mathematics
ISBN : 9783030544300

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Lie Models in Topology by Urtzi Buijs,Yves Félix,Aniceto Murillo,Daniel Tanré Pdf

Since the birth of rational homotopy theory, the possibility of extending the Quillen approach – in terms of Lie algebras – to a more general category of spaces, including the non-simply connected case, has been a challenge for the algebraic topologist community. Despite the clear Eckmann-Hilton duality between Quillen and Sullivan treatments, the simplicity in the realization of algebraic structures in the latter contrasts with the complexity required by the Lie algebra version. In this book, the authors develop new tools to address these problems. Working with complete Lie algebras, they construct, in a combinatorial way, a cosimplicial Lie model for the standard simplices. This is a key object, which allows the definition of a new model and realization functors that turn out to be homotopically equivalent to the classical Quillen functors in the simply connected case. With this, the authors open new avenues for solving old problems and posing new questions. This monograph is the winner of the 2020 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics.

Theory of Function Spaces III

Hans Triebel
Theory of Function Spaces III Book PDF

Author : Hans Triebel
Publisher : Springer Science & Business Media
Page : 433 pages
File Size : 46,5 Mb
Release : 2006-09-10
Category : Mathematics
ISBN : 9783764375829

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Theory of Function Spaces III by Hans Triebel Pdf

This volume presents the recent theory of function spaces, paying special attention to some recent developments related to neighboring areas such as numerics, signal processing, and fractal analysis. Local building blocks, in particular (non-smooth) atoms, quarks, wavelet bases and wavelet frames are considered in detail and applied to diverse problems, including a local smoothness theory, spaces on Lipschitz domains, and fractal analysis.

Algebraic Operads

Jean-Louis Loday,Bruno Vallette
Algebraic Operads Book PDF

Author : Jean-Louis Loday,Bruno Vallette
Publisher : Springer Science & Business Media
Page : 649 pages
File Size : 53,6 Mb
Release : 2012-08-08
Category : Mathematics
ISBN : 9783642303623

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Algebraic Operads by Jean-Louis Loday,Bruno Vallette Pdf

In many areas of mathematics some “higher operations” are arising. These havebecome so important that several research projects refer to such expressions. Higher operationsform new types of algebras. The key to understanding and comparing them, to creating invariants of their action is operad theory. This is a point of view that is 40 years old in algebraic topology, but the new trend is its appearance in several other areas, such as algebraic geometry, mathematical physics, differential geometry, and combinatorics. The present volume is the first comprehensive and systematic approach to algebraic operads. An operad is an algebraic device that serves to study all kinds of algebras (associative, commutative, Lie, Poisson, A-infinity, etc.) from a conceptual point of view. The book presents this topic with an emphasis on Koszul duality theory. After a modern treatment of Koszul duality for associative algebras, the theory is extended to operads. Applications to homotopy algebra are given, for instance the Homotopy Transfer Theorem. Although the necessary notions of algebra are recalled, readers are expected to be familiar with elementary homological algebra. Each chapter ends with a helpful summary and exercises. A full chapter is devoted to examples, and numerous figures are included. After a low-level chapter on Algebra, accessible to (advanced) undergraduate students, the level increases gradually through the book. However, the authors have done their best to make it suitable for graduate students: three appendices review the basic results needed in order to understand the various chapters. Since higher algebra is becoming essential in several research areas like deformation theory, algebraic geometry, representation theory, differential geometry, algebraic combinatorics, and mathematical physics, the book can also be used as a reference work by researchers.

Groups of Homotopy Self-Equivalences and Related Topics

Ken-ichi Maruyama,John W. Rutter
Groups of Homotopy Self Equivalences and Related Topics Book PDF

Author : Ken-ichi Maruyama,John W. Rutter
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 50,7 Mb
Release : 2001
Category : Homotopy equivalences
ISBN : 9780821826836

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Groups of Homotopy Self-Equivalences and Related Topics by Ken-ichi Maruyama,John W. Rutter Pdf

This volume offers the proceedings from the workshop held at the University of Milan (Italy) on groups of homotopy self-equivalences and related topics. The book comprises the articles relating current research on the group of homotopy self-equivalences, homotopy of function spaces, rational homotopy theory, classification of homotopy types, and equivariant homotopy theory. Mathematicians from many areas of the globe attended the workshops to discuss their research and to share ideas. Included are two specially-written articles, by J.W. Rutter, reviewing the work done in the area of homotopy self-equivalences since 1988. Included also is a bibliography of some 122 articles published since 1988 and a list of problems. This book is suitable for both advanced graduate students and researchers.

Homotopy Theory and Its Applications

Alejandro Adem,R. James Milgram,Douglas C. Ravenel
Homotopy Theory and Its Applications Book PDF

Author : Alejandro Adem,R. James Milgram,Douglas C. Ravenel
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 55,7 Mb
Release : 1995
Category : Homotopy theory
ISBN : 9780821803059

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Homotopy Theory and Its Applications by Alejandro Adem,R. James Milgram,Douglas C. Ravenel Pdf

This book is the result of a conference held to examine developments in homotopy theory in honor of Samuel Gitler in July 1993 (Cocoyoc, Mexico). It includes several research papers and three expository papers on various topics in homotopy theory. The research papers discuss the following: BL application of homotopy theory to group theory BL fiber bundle theory BL homotopy theory The expository papers consider the following topics: BL the Atiyah-Jones conjecture (by C. Boyer) BL classifying spaces of finite groups (by J. Martino) BL instanton moduli spaces (by J. Milgram) Homotopy Theory and Its Applications offers a distinctive account of how homotopy theoretic methods can be applied to a variety of interesting problems.

Symmetry for Elliptic PDEs

Alberto Farina
Symmetry for Elliptic PDEs Book PDF

Author : Alberto Farina
Publisher : American Mathematical Soc.
Page : 152 pages
File Size : 44,5 Mb
Release : 2010
Category : Differential equations, Elliptic
ISBN : 9780821848043

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Symmetry for Elliptic PDEs by Alberto Farina Pdf

Contains contributions from the INdAM School on Symmetry for Elliptic PDEs, which marked ""30 years after a conjecture of De Giorgi, and related problems"" and provided an opportunity for experts to discuss the state of the art and open questions on the subject.

Set Theory and Its Applications

Liljana Babinkostova
Set Theory and Its Applications Book PDF

Author : Liljana Babinkostova
Publisher : American Mathematical Soc.
Page : 346 pages
File Size : 49,7 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821848128

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Set Theory and Its Applications by Liljana Babinkostova Pdf

This book consists of several survey and research papers covering a wide range of topics in active areas of set theory and set theoretic topology. Some of the articles present, for the first time in print, knowledge that has been around for several years and known intimately to only a few experts. The surveys bring the reader up to date on the latest information in several areas that have been surveyed a decade or more ago. Topics covered in the volume include combinatorial and descriptive set theory, determinacy, iterated forcing, Ramsey theory, selection principles, set-theoretic topology, and universality, among others. Graduate students and researchers in logic, especially set theory, descriptive set theory, and set-theoretic topology, will find this book to be a very valuable reference.

Representation Theory and Mathematical Physics

Jeffrey Adams,Bong Lian,Siddhartha Sahi
Representation Theory and Mathematical Physics Book PDF

Author : Jeffrey Adams,Bong Lian,Siddhartha Sahi
Publisher : American Mathematical Soc.
Page : 404 pages
File Size : 46,8 Mb
Release : 2011-11-07
Category : Mathematics
ISBN : 9780821852460

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Representation Theory and Mathematical Physics by Jeffrey Adams,Bong Lian,Siddhartha Sahi Pdf

This volume contains the proceedings of the conference on Representation Theory and Mathematical Physics, in honor of Gregg Zuckerman's 60th birthday, held October 24-27, 2009, at Yale University. Lie groups and their representations play a fundamental role in mathematics, in particular because of connections to geometry, topology, number theory, physics, combinatorics, and many other areas. Representation theory is one of the cornerstones of the Langlands program in number theory, dating to the 1970s. Zuckerman's work on derived functors, the translation principle, and coherent continuation lie at the heart of the modern theory of representations of Lie groups. One of the major unsolved problems in representation theory is that of the unitary dual. The fact that there is, in principle, a finite algorithm for computing the unitary dual relies heavily on Zuckerman's work. In recent years there has been a fruitful interplay between mathematics and physics, in geometric representation theory, string theory, and other areas. New developments on chiral algebras, representation theory of affine Kac-Moody algebras, and the geometric Langlands correspondence are some of the focal points of this volume. Recent developments in the geometric Langlands program point to exciting connections between certain automorphic representations and dual fibrations in geometric mirror symmetry.

Arithmetic, Geometry, Cryptography and Coding Theory 2009

David R. Kohel,Robert Rolland
Arithmetic Geometry Cryptography and Coding Theory 2009 Book PDF

Author : David R. Kohel,Robert Rolland
Publisher : American Mathematical Soc.
Page : 178 pages
File Size : 40,8 Mb
Release : 2010
Category : Computers
ISBN : 9780821849552

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Arithmetic, Geometry, Cryptography and Coding Theory 2009 by David R. Kohel,Robert Rolland Pdf

This volume contains the proceedings of the 12th conference on Arithmetic, Geometry, Cryptography and Coding Theory, held in Marseille, France from March 30 to April 3, 2009, as well as the first Geocrypt conference, held in Pointe-a-Pitre, Guadeloupe from April 27 to May 1, 2009, and the European Science Foundation exploratory workshop on Curves, Coding Theory, and Cryptography, held in Marseille, France from March 25 to 29, 2009. The articles contained in this volume come from three related symposia organized by the group Arithmetique et Theorie de l'Information in Marseille. The topics cover arithmetic properties of curves and higher dimensional varieties with applications to codes and cryptography.

Advances in Non-Archimedean Analysis

Jesus Araujo-Gomez,Bertin Diarra,Alain Escassut
Advances in Non Archimedean Analysis Book PDF

Author : Jesus Araujo-Gomez,Bertin Diarra,Alain Escassut
Publisher : American Mathematical Soc.
Page : 294 pages
File Size : 47,9 Mb
Release : 2011
Category : Topological fields
ISBN : 9780821852910

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Advances in Non-Archimedean Analysis by Jesus Araujo-Gomez,Bertin Diarra,Alain Escassut Pdf

These collected articles feature recent developments in various areas of non-Archimedean analysis: Hilbert and Banach spaces, finite dimensional spaces, topological vector spaces and operator theory, strict topologies, spaces of continuous functions and of strictly differentiable functions, isomorphisms between Banach functions spaces, and measure and integration.

Theory of Function Spaces

Hans Triebel
Theory of Function Spaces Book PDF

Author : Hans Triebel
Publisher : Springer Science & Business Media
Page : 286 pages
File Size : 52,7 Mb
Release : 2010-08-20
Category : Science
ISBN : 9783034604154

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Theory of Function Spaces by Hans Triebel Pdf

The book deals with the two scales Bsp,q and Fsp,q of spaces of distributions, where ‐∞s∞ and 0p,q≤∞, which include many classical and modern spaces, such as Hölder spaces, Zygmund classes, Sobolev spaces, Besov spaces, Bessel-potential spaces, Hardy spaces and spaces of BMO-type. It is the main aim of this book to give a unified treatment of the corresponding spaces on the Euclidean n-space Rsubn

Introduction to Homotopy Theory

Martin Arkowitz
Introduction to Homotopy Theory Book PDF

Author : Martin Arkowitz
Publisher : Springer Science & Business Media
Page : 352 pages
File Size : 55,5 Mb
Release : 2011-07-25
Category : Mathematics
ISBN : 9781441973290

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Introduction to Homotopy Theory by Martin Arkowitz Pdf

This is a book in pure mathematics dealing with homotopy theory, one of the main branches of algebraic topology. The principal topics are as follows: Basic Homotopy; H-spaces and co-H-spaces; fibrations and cofibrations; exact sequences of homotopy sets, actions, and coactions; homotopy pushouts and pullbacks; classical theorems, including those of Serre, Hurewicz, Blakers-Massey, and Whitehead; homotopy Sets; homotopy and homology decompositions of spaces and maps; and obstruction theory. The underlying theme of the entire book is the Eckmann-Hilton duality theory. The book can be used as a text for the second semester of an advanced ungraduate or graduate algebraic topology course.

Introduction to Homotopy Theory

Paul Selick
Introduction to Homotopy Theory Book PDF

Author : Paul Selick
Publisher : American Mathematical Soc.
Page : 220 pages
File Size : 46,9 Mb
Release : 2008
Category : Mathematics
ISBN : 0821844369

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Introduction to Homotopy Theory by Paul Selick Pdf

Offers a summary for students and non-specialists who are interested in learning the basics of algebraic topology. This book covers fibrations and cofibrations, Hurewicz and cellular approximation theorems, topics in classical homotopy theory, simplicial sets, fiber bundles, Hopf algebras, and generalized homology and cohomology operations.