Sheaf Theory

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Sheaf Theory

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Author : Glen E. Bredon
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Sheaf Theory written by Glen E. Bredon and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This book is primarily concerned with the study of cohomology theories of general topological spaces with "general coefficient systems." Sheaves play several roles in this study. For example, they provide a suitable notion of "general coefficient systems." Moreover, they furnish us with a common method of defining various cohomology theories and of comparison between different cohomology theories. The parts of the theory of sheaves covered here are those areas important to algebraic topology. Sheaf theory is also important in other fields of mathematics, notably algebraic geometry, but that is outside the scope of the present book. Thus a more descriptive title for this book might have been Algebraic Topology from the Point of View of Sheaf Theory. Several innovations will be found in this book. Notably, the concept of the "tautness" of a subspace (an adaptation of an analogous notion of Spanier to sheaf-theoretic cohomology) is introduced and exploited throughout the book. The factthat sheaf-theoretic cohomology satisfies 1 the homotopy property is proved for general topological spaces. Also, relative cohomology is introduced into sheaf theory. Concerning relative cohomology, it should be noted that sheaf-theoretic cohomology is usually considered as a "single space" theory.

Categories And Sheaves

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Author : Masaki Kashiwara
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-10-20

Categories And Sheaves written by Masaki Kashiwara and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-10-20 with Mathematics categories.

Categories and sheaves appear almost frequently in contemporary advanced mathematics. This book covers categories, homological algebra and sheaves in a systematic manner starting from scratch and continuing with full proofs to the most recent results in the literature, and sometimes beyond. The authors present the general theory of categories and functors, emphasizing inductive and projective limits, tensor categories, representable functors, ind-objects and localization.

Sheaves On Manifolds

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Author : Masaki Kashiwara
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-05-01

Sheaves On Manifolds written by Masaki Kashiwara and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-05-01 with Mathematics categories.

Sheaf Theory is modern, active field of mathematics at the intersection of algebraic topology, algebraic geometry and partial differential equations. This volume offers a comprehensive and self-contained treatment of Sheaf Theory from the basis up, with emphasis on the microlocal point of view. From the reviews: "Clearly and precisely written, and contains many interesting ideas: it describes a whole, largely new branch of mathematics." –Bulletin of the L.M.S.

Manifolds Sheaves And Cohomology

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Author : Torsten Wedhorn
language : en
Publisher: Springer
Release Date : 2016-07-25

Manifolds Sheaves And Cohomology written by Torsten Wedhorn and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-25 with Mathematics categories.

This book explains techniques that are essential in almost all branches of modern geometry such as algebraic geometry, complex geometry, or non-archimedian geometry. It uses the most accessible case, real and complex manifolds, as a model. The author especially emphasizes the difference between local and global questions. Cohomology theory of sheaves is introduced and its usage is illustrated by many examples.

Sheaf Theory Through Examples

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Author : Daniel Rosiak
language : en
Publisher: MIT Press
Release Date : 2022-10-25

Sheaf Theory Through Examples written by Daniel Rosiak and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-25 with Mathematics categories.

An approachable introduction to elementary sheaf theory and its applications beyond pure math. Sheaves are mathematical constructions concerned with passages from local properties to global ones. They have played a fundamental role in the development of many areas of modern mathematics, yet the broad conceptual power of sheaf theory and its wide applicability to areas beyond pure math have only recently begun to be appreciated. Taking an applied category theory perspective, Sheaf Theory through Examples provides an approachable introduction to elementary sheaf theory and examines applications including n-colorings of graphs, satellite data, chess problems, Bayesian networks, self-similar groups, musical performance, complexes, and much more. With an emphasis on developing the theory via a wealth of well-motivated and vividly illustrated examples, Sheaf Theory through Examples supplements the formal development of concepts with philosophical reflections on topology, category theory, and sheaf theory, alongside a selection of advanced topics and examples that illustrate ideas like cellular sheaf cohomology, toposes, and geometric morphisms. Sheaf Theory through Examples seeks to bridge the powerful results of sheaf theory as used by mathematicians and real-world applications, while also supplementing the technical matters with a unique philosophical perspective attuned to the broader development of ideas.

D Modules Perverse Sheaves And Representation Theory

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Author : Kiyoshi Takeuchi
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-12

D Modules Perverse Sheaves And Representation Theory written by Kiyoshi Takeuchi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-12 with Mathematics categories.

D-modules continues to be an active area of stimulating research in such mathematical areas as algebraic, analysis, differential equations, and representation theory. Key to D-modules, Perverse Sheaves, and Representation Theory is the authors' essential algebraic-analytic approach to the theory, which connects D-modules to representation theory and other areas of mathematics. To further aid the reader, and to make the work as self-contained as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. The book is intended to serve graduate students in a classroom setting and as self-study for researchers in algebraic geometry, representation theory.

Handbook Of Categorical Algebra Volume 3 Sheaf Theory

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Author : Francis Borceux
language : en
Publisher: Cambridge University Press
Release Date : 1994-12-08

Handbook Of Categorical Algebra Volume 3 Sheaf Theory written by Francis Borceux and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-12-08 with Mathematics categories.

The Handbook of Categorical Algebra is intended to give, in three volumes, a rather detailed account of what, ideally, everybody working in category theory should know, whatever the specific topic of research they have chosen. The book is planned also to serve as a reference book for both specialists in the field and all those using category theory as a tool. Volume 3 begins with the essential aspects of the theory of locales, proceeding to a study in chapter 2 of the sheaves on a locale and on a topological space, in their various equivalent presentations: functors, etale maps or W-sets. Next, this situation is generalized to the case of sheaves on a site and the corresponding notion of Grothendieck topos is introduced. Chapter 4 relates the theory of Grothendieck toposes with that of accessible categories and sketches, by proving the existence of a classifying topos for all coherent theories.

Introduction To The Theory Of Schemes

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Author : Yuri I. Manin
language : en
Publisher: Springer
Release Date : 2018-05-15

Introduction To The Theory Of Schemes written by Yuri I. Manin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-15 with Mathematics categories.

This English edition of Yuri I. Manin's well-received lecture notes provides a concise but extremely lucid exposition of the basics of algebraic geometry and sheaf theory. The lectures were originally held in Moscow in the late 1960s, and the corresponding preprints were widely circulated among Russian mathematicians. This book will be of interest to students majoring in algebraic geometry and theoretical physics (high energy physics, solid body, astrophysics) as well as to researchers and scholars in these areas. "This is an excellent introduction to the basics of Grothendieck's theory of schemes; the very best first reading about the subject that I am aware of. I would heartily recommend every grad student who wants to study algebraic geometry to read it prior to reading more advanced textbooks."- Alexander Beilinson

Sheaf Theory

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Author : Glen E. Bredon
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-01-24

Sheaf Theory written by Glen E. Bredon and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-24 with Mathematics categories.

Primarily concerned with the study of cohomology theories of general topological spaces with "general coefficient systems", the parts of sheaf theory covered here are those areas important to algebraic topology. Among the many innovations in this book, the concept of the "tautness" of a subspace is introduced and exploited; the fact that sheaf theoretic cohomology satisfies the homotopy property is proved for general topological spaces; and relative cohomology is introduced into sheaf theory. A list of exercises at the end of each chapter helps students to learn the material, and solutions to many of the exercises are given in an appendix. This new edition of a classic has been substantially rewritten and now includes some 80 additional examples and further explanatory material, as well as new sections on Cech cohomology, the Oliver transfer, intersection theory, generalised manifolds, locally homogeneous spaces, homological fibrations and p- adic transformation groups. Readers should have a thorough background in elementary homological algebra and in algebraic topology.

Topology Of Singular Spaces And Constructible Sheaves

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Author : Jörg Schürmann
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-10-24

Topology Of Singular Spaces And Constructible Sheaves written by Jörg Schürmann and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-10-24 with Mathematics categories.

Assuming that the reader is familiar with sheaf theory, the book gives a self-contained introduction to the theory of constructible sheaves related to many kinds of singular spaces, such as cell complexes, triangulated spaces, semialgebraic and subanalytic sets, complex algebraic or analytic sets, stratified spaces, and quotient spaces. The relation to the underlying geometrical ideas are worked out in detail, together with many applications to the topology of such spaces. All chapters have their own detailed introduction, containing the main results and definitions, illustrated in simple terms by a number of examples. The technical details of the proof are postponed to later sections, since these are not needed for the applications.