Nash Manifolds

Author : Masahiro Shiota
Publisher : Springer
Page : 229 pages
File Size : 49,8 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540477631

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Nash Manifolds by Masahiro Shiota Pdf

A Nash manifold denotes a real manifold furnished with algebraic structure, following a theorem of Nash that a compact differentiable manifold can be imbedded in a Euclidean space so that the image is precisely such a manifold. This book, in which almost all results are very recent or unpublished, is an account of the theory of Nash manifolds, whose properties are clearer and more regular than those of differentiable or PL manifolds. Basic to the theory is an algebraic analogue of Whitney's Approximation Theorem. This theorem induces a "finiteness" of Nash manifold structures and differences between Nash and differentiable manifolds. The point of view of the author is topological. However the proofs also require results and techniques from other domains so elementary knowledge of commutative algebra, several complex variables, differential topology, PL topology and real singularities is required of the reader. The book is addressed to graduate students and researchers in differential topology and real algebraic geometry.

Author : W. L. Marar
Publisher : CRC Press
Page : 228 pages
File Size : 40,9 Mb
Release : 1995-10-18
Category : Mathematics
ISBN : 0582277809

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Real and Complex Singularities by W. L. Marar Pdf

Much progress has been made recently in a number of areas by the application of new geometrical methods arising from advances in singularity theory. This collection of invited papers presented at the 3rd International Workshop on Real and Complex Singularities, held in August 1994 at ICMSC-USP (Sao Carlos), documents the geometric study of singularities and its applications.

Author : Fabrizio Broglia
Publisher : Walter de Gruyter
Page : 285 pages
File Size : 55,7 Mb
Release : 2011-10-10
Category : Mathematics
ISBN : 9783110811117

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Lectures in Real Geometry by Fabrizio Broglia Pdf

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

Author : Riccardo Benedetti
Publisher : American Mathematical Soc.
Page : 425 pages
File Size : 54,8 Mb
Release : 2021-10-27
Category : Education
ISBN : 9781470466749

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Lectures on Differential Topology by Riccardo Benedetti Pdf

This book gives a comprehensive introduction to the theory of smooth manifolds, maps, and fundamental associated structures with an emphasis on “bare hands” approaches, combining differential-topological cut-and-paste procedures and applications of transversality. In particular, the smooth cobordism cup-product is defined from scratch and used as the main tool in a variety of settings. After establishing the fundamentals, the book proceeds to a broad range of more advanced topics in differential topology, including degree theory, the Poincaré-Hopf index theorem, bordism-characteristic numbers, and the Pontryagin-Thom construction. Cobordism intersection forms are used to classify compact surfaces; their quadratic enhancements are developed and applied to studying the homotopy groups of spheres, the bordism group of immersed surfaces in a 3-manifold, and congruences mod 16 for the signature of intersection forms of 4-manifolds. Other topics include the high-dimensional h h-cobordism theorem stressing the role of the “Whitney trick”, a determination of the singleton bordism modules in low dimensions, and proofs of parallelizability of orientable 3-manifolds and the Lickorish-Wallace theorem. Nash manifolds and Nash's questions on the existence of real algebraic models are also discussed. This book will be useful as a textbook for beginning masters and doctoral students interested in differential topology, who have finished a standard undergraduate mathematics curriculum. It emphasizes an active learning approach, and exercises are included within the text as part of the flow of ideas. Experienced readers may use this book as a source of alternative, constructive approaches to results commonly presented in more advanced contexts with specialized techniques.

Author : Anthony Bak,Masaharu Morimoto,Fumihiro Ushitaki
Publisher : Springer Science & Business Media
Page : 272 pages
File Size : 42,5 Mb
Release : 2002-07-31
Category : Mathematics
ISBN : 1402007833

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Current Trends in Transformation Groups by Anthony Bak,Masaharu Morimoto,Fumihiro Ushitaki Pdf

This book provides an overview of some of the most active topics in the theory of transformation groups over the past decades and stresses advances obtained in the last dozen years. The emphasis is on actions of Lie groups on manifolds and CW complexes. Manifolds and actions of Lie groups on them are studied in the linear, semialgebraic, definable, analytic, smooth, and topological categories. Equivalent vector bundles play an important role. The work is divided into fifteen articles and will be of interest to anyone researching or studying transformations groups. The references make it easy to find details and original accounts of the topics surveyed, including tools and theories used in these accounts.

Author : Helge Holden,Ragni Piene
Publisher : Springer
Page : 774 pages
File Size : 55,9 Mb
Release : 2019-02-23
Category : Mathematics
ISBN : 9783319990286

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The Abel Prize 2013-2017 by Helge Holden,Ragni Piene Pdf

The book presents the winners of the Abel Prize in mathematics for the period 2013–17: Pierre Deligne (2013); Yakov G. Sinai (2014); John Nash Jr. and Louis Nirenberg (2015); Sir Andrew Wiles (2016); and Yves Meyer (2017). The profiles feature autobiographical information as well as a scholarly description of each mathematician’s work. In addition, each profile contains a Curriculum Vitae, a complete bibliography, and the full citation from the prize committee. The book also includes photos for the period 2003–2017 showing many of the additional activities connected with the Abel Prize. As an added feature, video interviews with the Laureates as well as videos from the prize ceremony are provided at an accompanying website (http://extras.springer.com/). This book follows on The Abel Prize: 2003-2007. The First Five Years (Springer, 2010) and The Abel Prize 2008-2012 (Springer 2014), which profile the work of the previous Abel Prize winners.

Author : A. Broer
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 48,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401591317

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Representation Theories and Algebraic Geometry by A. Broer Pdf

The 12 lectures presented in Representation Theories and Algebraic Geometry focus on the very rich and powerful interplay between algebraic geometry and the representation theories of various modern mathematical structures, such as reductive groups, quantum groups, Hecke algebras, restricted Lie algebras, and their companions. This interplay has been extensively exploited during recent years, resulting in great progress in these representation theories. Conversely, a great stimulus has been given to the development of such geometric theories as D-modules, perverse sheafs and equivariant intersection cohomology. The range of topics covered is wide, from equivariant Chow groups, decomposition classes and Schubert varieties, multiplicity free actions, convolution algebras, standard monomial theory, and canonical bases, to annihilators of quantum Verma modules, modular representation theory of Lie algebras and combinatorics of representation categories of Harish-Chandra modules.

Author : Olga Kharlampovich,Rizos Sklinos
Publisher : Walter de Gruyter GmbH & Co KG
Page : 250 pages
File Size : 51,8 Mb
Release : 2021-05-10
Category : Mathematics
ISBN : 9783110719765

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Groups and Model Theory by Olga Kharlampovich,Rizos Sklinos Pdf

This monograph provides an overview of developments in group theory motivated by model theory by key international researchers in the field. Topics covered include: stable groups and generalizations, model theory of nonabelian free groups and of rigid solvable groups, pseudofinite groups, approximate groups, topological dynamics, groups interpreting the arithmetic. The book is intended for mathematicians and graduate students in group theory and model theory. The book follows the course of the GAGTA (Geometric and Asymptotic Group Theory with Applications) conference series. The first book, "Complexity and Randomness in Group Theory. GAGTA book 1," can be found here: http://www.degruyter.com/books/978-3-11-066491-1 .

Author : Toshisumi Fukui,Shuichi Izumiya,Satoshi Koike,Toshisumi Fukuda
Publisher : CRC Press
Page : 236 pages
File Size : 55,7 Mb
Release : 1997-12-12
Category : Mathematics
ISBN : 0582328748

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Real Analytic and Algebraic Singularities by Toshisumi Fukui,Shuichi Izumiya,Satoshi Koike,Toshisumi Fukuda Pdf

This book contains a collection of papers covering recent progress in a number of areas of singularity theory. Topics include blow analyticity, recent progress in the research on equivalence relations of maps and functions, sufficiency of jets, and the transversality theorem. . Geometric and analytic studies of partial differential equations have been developed independently of one another, but the shock wave solutions appearing in natural phenomena are not well understood. Singularity theory may unify these studies and a survey based on this viewpoint is presented in which a new notion of weak solution is introduced. There are also reports on the recent progress in Zariski's conjecture on multiplicities of hypersurfaces, transcendency of analytic sets and on the topology of weighted homogeneous polynomials. This book will be of particular interest to specialists in singularities, partial differential equations, algebraic geometry and control theory.

Author : Greg Friedman
Publisher : Cambridge University Press
Page : 491 pages
File Size : 44,8 Mb
Release : 2011-03-28
Category : Mathematics
ISBN : 9780521191678

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Topology of Stratified Spaces by Greg Friedman Pdf

This book explores the study of singular spaces using techniques from areas within geometry and topology and the interactions among them.

Author : Jörg Schürmann
Publisher : Birkhäuser
Page : 461 pages
File Size : 53,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034880619

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Topology of Singular Spaces and Constructible Sheaves by Jörg Schürmann Pdf

This volume is based on the lecture notes of six courses delivered at a Cimpa Summer School in Temuco, Chile, in January 2001. Leading experts contribute with introductory articles covering a broad area in probability and its applications, such as mathematical physics and mathematics of finance. Written at graduate level, the lectures touch the latest advances on each subject, ranging from classical probability theory to modern developments. Thus the book will appeal to students, teachers and researchers working in probability theory or related fields.

Author : Jacek Bochnak,Michel Coste,Marie-Francoise Roy
Publisher : Springer Science & Business Media
Page : 429 pages
File Size : 53,5 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9783662037188

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Real Algebraic Geometry by Jacek Bochnak,Michel Coste,Marie-Francoise Roy Pdf

The present volume is a translation, revision and updating of our book (pub lished in French) with the title "Geometrie Algebrique Reelle". Since its pub lication in 1987 the theory has made advances in several directions. There have also been new insights into material already in the French edition. Many of these advances and insights have been incorporated in this English version of the book, so that it may be viewed as being substantially different from the original. We wish to thank Michael Buchner for his careful reading of the text and for his linguistic corrections and stylistic improvements. The initial Jb. TEiX file was prepared by Thierry van Effelterre. The three authors participate in the European research network "Real Algebraic and Analytic Geometry". The first author was partially supported by NATO Collaborative Research Grant 960011. Jacek Bochnak April 1998 Michel Coste Marie-Pranroise Roy Table of Contents Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. Ordered Fields, Real Closed Fields . . . . . . . . . . . . . . . . . . . . . . . 7 1. 1 Ordered Fields, Real Fields . . . . . " . . . . . . . . . . . . . . . . . . . . . . . 7 1. 2 Real Closed Fields. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1. 3 Real Closure of an Ordered Field. . . . . . . . . . . . . . . . . . . . . . . . . 14 1. 4 The Tarski-Seidenberg Principle. . . . . . . . . . . . . . . . . . . . . . . . . . 17 2. Semi-algebraic Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2. 1 Algebraic and Semi-algebraic Sets. . . . . . . . . . . . . . . . . . . . . . . . 23 2. 2 Projection of Semi-algebraic Sets. Semi-algebraic Mappings. . 26 2. 3 Decomposition of Semi-algebraic Sets. . . . . . . . . . . . . . . . . . . . . 30 2. 4 Connectedness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2. 5 Closed and Bounded Semi-algebraic Sets. Curve-selection Lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2. 6 Continuous Semi-algebraic Functions. Lojasiewicz's Inequality 42 2. 7 Separation of Closed Semi-algebraic Sets. . . . . . . . . . . . . . . . . .

Author : Anonim
Publisher : Unknown
Page : 1326 pages
File Size : 47,5 Mb
Release : 1832
Category : Law reports, digests, etc
ISBN : HARVARD:HL04KQ

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Records and Briefs of the United States Supreme Court by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 40,7 Mb
Release : 2024-07-01
Category : Electronic
ISBN : 9789814475983

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Real and Complex Singularities by Anonim Pdf

Author : I.M. James
Publisher : Elsevier
Page : 1067 pages
File Size : 45,7 Mb
Release : 1999-08-24
Category : Mathematics
ISBN : 9780080534077

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History of Topology by I.M. James Pdf

Topology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincaré who "gave topology wings" in a classic series of articles published around the turn of the century. While the earlier history, sometimes called the prehistory, is also considered, this volume is mainly concerned with the more recent history of topology, from Poincaré onwards.As will be seen from the list of contents the articles cover a wide range of topics. Some are more technical than others, but the reader without a great deal of technical knowledge should still find most of the articles accessible. Some are written by professional historians of mathematics, others by historically-minded mathematicians, who tend to have a different viewpoint.