Manifolds Sheaves And Cohomology

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Manifolds, Sheaves, and Cohomology

Torsten Wedhorn
Manifolds Sheaves and Cohomology Book PDF

Author : Torsten Wedhorn
Publisher : Springer
Page : 366 pages
File Size : 50,5 Mb
Release : 2016-07-25
Category : Mathematics
ISBN : 9783658106331

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Manifolds, Sheaves, and Cohomology by Torsten Wedhorn Pdf

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.

Sheaves on Manifolds

Masaki Kashiwara,Pierre Schapira
Sheaves on Manifolds Book PDF

Author : Masaki Kashiwara,Pierre Schapira
Publisher : Springer Science & Business Media
Page : 522 pages
File Size : 42,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662026618

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Sheaves on Manifolds by Masaki Kashiwara,Pierre Schapira Pdf

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.

Algebraic Geometry over the Complex Numbers

Donu Arapura
Algebraic Geometry over the Complex Numbers Book PDF

Author : Donu Arapura
Publisher : Springer Science & Business Media
Page : 326 pages
File Size : 45,9 Mb
Release : 2012-02-15
Category : Mathematics
ISBN : 9781461418092

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Algebraic Geometry over the Complex Numbers by Donu Arapura Pdf

This is a relatively fast paced graduate level introduction to complex algebraic geometry, from the basics to the frontier of the subject. It covers sheaf theory, cohomology, some Hodge theory, as well as some of the more algebraic aspects of algebraic geometry. The author frequently refers the reader if the treatment of a certain topic is readily available elsewhere but goes into considerable detail on topics for which his treatment puts a twist or a more transparent viewpoint. His cases of exploration and are chosen very carefully and deliberately. The textbook achieves its purpose of taking new students of complex algebraic geometry through this a deep yet broad introduction to a vast subject, eventually bringing them to the forefront of the topic via a non-intimidating style.

Cohomology and Differential Forms

Izu Vaisman
Cohomology and Differential Forms Book PDF

Author : Izu Vaisman
Publisher : Courier Dover Publications
Page : 304 pages
File Size : 43,5 Mb
Release : 2016-07-28
Category : Mathematics
ISBN : 9780486815121

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Cohomology and Differential Forms by Izu Vaisman Pdf

Self-contained development of cohomological theory of manifolds with various sheaves and its application to differential geometry covers categories and functions, sheaves and cohomology, fiber and vector bundles, and cohomology classes and differential forms. 1973 edition.

Sheaf Theory

Glen E. Bredon
Sheaf Theory Book PDF

Author : Glen E. Bredon
Publisher : Springer Science & Business Media
Page : 518 pages
File Size : 46,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461206477

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Sheaf Theory by Glen E. Bredon Pdf

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.

Geometry of Vector Sheaves

Anastasios Mallios
Geometry of Vector Sheaves Book PDF

Author : Anastasios Mallios
Publisher : Springer Science & Business Media
Page : 457 pages
File Size : 42,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401150064

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Geometry of Vector Sheaves by Anastasios Mallios Pdf

This two-volume monograph obtains fundamental notions and results of the standard differential geometry of smooth (CINFINITY) manifolds, without using differential calculus. Here, the sheaf-theoretic character is emphasised. This has theoretical advantages such as greater perspective, clarity and unification, but also practical benefits ranging from elementary particle physics, via gauge theories and theoretical cosmology (`differential spaces'), to non-linear PDEs (generalised functions). Thus, more general applications, which are no longer `smooth' in the classical sense, can be coped with. The treatise might also be construed as a new systematic endeavour to confront the ever-increasing notion that the `world around us is far from being smooth enough'. Audience: This work is intended for postgraduate students and researchers whose work involves differential geometry, global analysis, analysis on manifolds, algebraic topology, sheaf theory, cohomology, functional analysis or abstract harmonic analysis.

Global Calculus

S. Ramanan
Global Calculus Book PDF

Author : S. Ramanan
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 42,9 Mb
Release : 2005
Category : Analytic spaces
ISBN : 9780821837023

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Global Calculus by S. Ramanan Pdf

The power that analysis, topology and algebra bring to geometry has revolutionised the way geometers and physicists look at conceptual problems. Some of the key ingredients in this interplay are sheaves, cohomology, Lie groups, connections and differential operators. In Global Calculus, the appropriate formalism for these topics is laid out with numerous examples and applications by one of the experts in differential and algebraic geometry. Ramanan has chosen an uncommon but natural path through the subject. In this almost completely self-contained account, these topics are developed from scratch. The basics of Fourier transforms, Sobolev theory and interior regularity are proved at the same time as symbol calculus, culminating in beautiful results in global analysis, real and complex. Many new perspectives on traditional and modern questions of differential analysis and geometry are the hallmarks of the book. The book is suitable for a first year graduate course on Global Analysis.

Sheaves in Topology

Alexandru Dimca
Sheaves in Topology Book PDF

Author : Alexandru Dimca
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 41,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642188688

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Sheaves in Topology by Alexandru Dimca Pdf

Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds. This introduction to the subject can be regarded as a textbook on modern algebraic topology, treating the cohomology of spaces with sheaf (as opposed to constant) coefficients. The author helps readers progress quickly from the basic theory to current research questions, thoroughly supported along the way by examples and exercises.

Foundations of Differentiable Manifolds and Lie Groups

Frank W. Warner
Foundations of Differentiable Manifolds and Lie Groups Book PDF

Author : Frank W. Warner
Publisher : Springer Science & Business Media
Page : 283 pages
File Size : 40,8 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475717990

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Foundations of Differentiable Manifolds and Lie Groups by Frank W. Warner Pdf

Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. Coverage includes differentiable manifolds, tensors and differentiable forms, Lie groups and homogenous spaces, and integration on manifolds. The book also provides a proof of the de Rham theorem via sheaf cohomology theory and develops the local theory of elliptic operators culminating in a proof of the Hodge theorem.

Smooth Manifolds and Observables

Jet Nestruev
Smooth Manifolds and Observables Book PDF

Author : Jet Nestruev
Publisher : Springer Nature
Page : 433 pages
File Size : 47,5 Mb
Release : 2020-09-10
Category : Mathematics
ISBN : 9783030456504

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Smooth Manifolds and Observables by Jet Nestruev Pdf

This book gives an introduction to fiber spaces and differential operators on smooth manifolds. Over the last 20 years, the authors developed an algebraic approach to the subject and they explain in this book why differential calculus on manifolds can be considered as an aspect of commutative algebra. This new approach is based on the fundamental notion of observable which is used by physicists and will further the understanding of the mathematics underlying quantum field theory.

From Calculus to Cohomology

Ib H. Madsen,Jxrgen Tornehave
From Calculus to Cohomology Book PDF

Author : Ib H. Madsen,Jxrgen Tornehave
Publisher : Cambridge University Press
Page : 302 pages
File Size : 46,9 Mb
Release : 1997-03-13
Category : Mathematics
ISBN : 0521589568

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From Calculus to Cohomology by Ib H. Madsen,Jxrgen Tornehave Pdf

An introductory textbook on cohomology and curvature with emphasis on applications.

Introduction to Complex Manifolds

John M. Lee
Introduction to Complex Manifolds Book PDF

Author : John M. Lee
Publisher : American Mathematical Society
Page : 377 pages
File Size : 47,6 Mb
Release : 2024-05-15
Category : Mathematics
ISBN : 9781470477820

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Introduction to Complex Manifolds by John M. Lee Pdf

Complex manifolds are smooth manifolds endowed with coordinate charts that overlap holomorphically. They have deep and beautiful applications in many areas of mathematics. This book is an introduction to the concepts, techniques, and main results about complex manifolds (mainly compact ones), and it tells a story. Starting from familiarity with smooth manifolds and Riemannian geometry, it gradually explains what is different about complex manifolds and develops most of the main tools for working with them, using the Kodaira embedding theorem as a motivating project throughout. The approach and style will be familiar to readers of the author's previous graduate texts: new concepts are introduced gently, with as much intuition and motivation as possible, always relating new concepts to familiar old ones, with plenty of examples. The main prerequisite is familiarity with the basic results on topological, smooth, and Riemannian manifolds. The book is intended for graduate students and researchers in differential geometry, but it will also be appreciated by students of algebraic geometry who wish to understand the motivations, analogies, and analytic results that come from the world of differential geometry.

Derived Functors And Sheaf Cohomology

Ugo Bruzzo,Beatriz Grana Otero
Derived Functors And Sheaf Cohomology Book PDF

Author : Ugo Bruzzo,Beatriz Grana Otero
Publisher : World Scientific
Page : 214 pages
File Size : 49,8 Mb
Release : 2020-03-10
Category : Mathematics
ISBN : 9789811207303

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Derived Functors And Sheaf Cohomology by Ugo Bruzzo,Beatriz Grana Otero Pdf

The aim of the book is to present a precise and comprehensive introduction to the basic theory of derived functors, with an emphasis on sheaf cohomology and spectral sequences. It keeps the treatment as simple as possible, aiming at the same time to provide a number of examples, mainly from sheaf theory, and also from algebra.The first part of the book provides the foundational material: Chapter 1 deals with category theory and homological algebra. Chapter 2 is devoted to the development of the theory of derived functors, based on the notion of injective object. In particular, the universal properties of derived functors are stressed, with a view to make the proofs in the following chapters as simple and natural as possible. Chapter 3 provides a rather thorough introduction to sheaves, in a general topological setting. Chapter 4 introduces sheaf cohomology as a derived functor, and, after also defining Čech cohomology, develops a careful comparison between the two cohomologies which is a detailed analysis not easily available in the literature. This comparison is made using general, universal properties of derived functors. This chapter also establishes the relations with the de Rham and Dolbeault cohomologies. Chapter 5 offers a friendly approach to the rather intricate theory of spectral sequences by means of the theory of derived triangles, which is precise and relatively easy to grasp. It also includes several examples of specific spectral sequences. Readers will find exercises throughout the text, with additional exercises included at the end of each chapter.

Intersection Homology & Perverse Sheaves

Laurenţiu G. Maxim
Intersection Homology Perverse Sheaves Book PDF

Author : Laurenţiu G. Maxim
Publisher : Springer Nature
Page : 270 pages
File Size : 48,5 Mb
Release : 2019-11-30
Category : Mathematics
ISBN : 9783030276447

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Intersection Homology & Perverse Sheaves by Laurenţiu G. Maxim Pdf

This textbook provides a gentle introduction to intersection homology and perverse sheaves, where concrete examples and geometric applications motivate concepts throughout. By giving a taste of the main ideas in the field, the author welcomes new readers to this exciting area at the crossroads of topology, algebraic geometry, analysis, and differential equations. Those looking to delve further into the abstract theory will find ample references to facilitate navigation of both classic and recent literature. Beginning with an introduction to intersection homology from a geometric and topological viewpoint, the text goes on to develop the sheaf-theoretical perspective. Then algebraic geometry comes to the fore: a brief discussion of constructibility opens onto an in-depth exploration of perverse sheaves. Highlights from the following chapters include a detailed account of the proof of the Beilinson–Bernstein–Deligne–Gabber (BBDG) decomposition theorem, applications of perverse sheaves to hypersurface singularities, and a discussion of Hodge-theoretic aspects of intersection homology via Saito’s deep theory of mixed Hodge modules. An epilogue offers a succinct summary of the literature surrounding some recent applications. Intersection Homology & Perverse Sheaves is suitable for graduate students with a basic background in topology and algebraic geometry. By building context and familiarity with examples, the text offers an ideal starting point for those entering the field. This classroom-tested approach opens the door to further study and to current research.

Hodge Theory and Complex Algebraic Geometry I: Volume 1

Claire Voisin
Hodge Theory and Complex Algebraic Geometry I Volume 1 Book PDF

Author : Claire Voisin
Publisher : Cambridge University Press
Page : 336 pages
File Size : 46,9 Mb
Release : 2002-12-05
Category : Mathematics
ISBN : 9781139437691

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Hodge Theory and Complex Algebraic Geometry I: Volume 1 by Claire Voisin Pdf

The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure. The book starts with basic material on complex variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory, the latter being treated in a more theoretical way than is usual in geometry. The author then proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The book culminates with the Hodge decomposition theorem. The meanings of these results are investigated in several directions. Completely self-contained, the book is ideal for students, while its content gives an account of Hodge theory and complex algebraic geometry as has been developed by P. Griffiths and his school, by P. Deligne, and by S. Bloch. The text is complemented by exercises which provide useful results in complex algebraic geometry.