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 : 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.

Sheaf Theory

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Author : B. R. Tennison
language : en
Publisher: Cambridge University Press
Release Date : 1975-12-18

Sheaf Theory written by B. R. Tennison 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 1975-12-18 with Mathematics categories.

Sheaf theory provides a means of discussing many different kinds of geometric objects in respect of the connection between their local and global properties. It finds its main applications in topology and modern algebraic geometry where it has been used as a tool for solving, with great success, several long-standing problems. This text is based on a lecture course for graduate pure mathematicians which builds up enough of the foundations of sheaf theory to give a broad definition of manifold, covering as special cases the algebraic geometer's schemes as well as the topological, differentiable and analytic kinds, and to define sheaf cohomology for application to such objects. Exercises are provided at the end of each chapter and at various places in the text. Hints and solutions to some of them are given at the end of the book.

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.

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.

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.

Applications Of Sheaves

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Author : M. P. Fourman
language : en
Publisher: Springer
Release Date : 2006-11-15

Applications Of Sheaves written by M. P. Fourman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

Elements Of Sheaf Theory

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Author : Daniel Bert Abrams
language : en
Publisher:
Release Date : 1987

Elements Of Sheaf Theory written by Daniel Bert Abrams and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Homology theory categories.

Sheaves On Graphs Their Homological Invariants And A Proof Of The Hanna Neumann Conjecture

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Author : Joel Friedman
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-12-20

Sheaves On Graphs Their Homological Invariants And A Proof Of The Hanna Neumann Conjecture written by Joel Friedman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-20 with Mathematics categories.

In this paper the author establishes some foundations regarding sheaves of vector spaces on graphs and their invariants, such as homology groups and their limits. He then uses these ideas to prove the Hanna Neumann Conjecture of the 1950s; in fact, he proves a strengthened form of the conjecture.

Encyclopaedia Of Mathematics

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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Encyclopaedia Of Mathematics written by Michiel Hazewinkel 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 ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

Reflectors And Localization

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Author : F. Van Oystaeyen
language : en
Publisher:
Release Date : 1979

Reflectors And Localization written by F. Van Oystaeyen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.