Sheaves On Manifolds

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.

Author : Torsten Wedhorn
Publisher : Springer
Page : 366 pages
File Size : 49,8 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.

Author : Masaki Kashiwara,Pierre Schapira
Publisher : Springer Science & Business Media
Page : 496 pages
File Size : 48,9 Mb
Release : 2005-12-19
Category : Mathematics
ISBN : 9783540279501

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Categories and Sheaves by Masaki Kashiwara,Pierre Schapira Pdf

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.

Author : Anastasios Mallios
Publisher : Springer Science & Business Media
Page : 457 pages
File Size : 54,7 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.

Author : Donu Arapura
Publisher : Springer Science & Business Media
Page : 326 pages
File Size : 53,6 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.

Author : S. Ramanan
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 40,7 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.

Author : Alexandru Dimca
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 45,8 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.

Author : Eckart Viehweg
Publisher : Springer Science & Business Media
Page : 329 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642797453

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Quasi-projective Moduli for Polarized Manifolds by Eckart Viehweg Pdf

The concept of moduli goes back to B. Riemann, who shows in [68] that the isomorphism class of a Riemann surface of genus 9 ~ 2 depends on 3g - 3 parameters, which he proposes to name "moduli". A precise formulation of global moduli problems in algebraic geometry, the definition of moduli schemes or of algebraic moduli spaces for curves and for certain higher dimensional manifolds have only been given recently (A. Grothendieck, D. Mumford, see [59]), as well as solutions in some cases. It is the aim of this monograph to present methods which allow over a field of characteristic zero to construct certain moduli schemes together with an ample sheaf. Our main source of inspiration is D. Mumford's "Geometric In variant Theory". We will recall the necessary tools from his book [59] and prove the "Hilbert-Mumford Criterion" and some modified version for the stability of points under group actions. As in [78], a careful study of positivity proper ties of direct image sheaves allows to use this criterion to construct moduli as quasi-projective schemes for canonically polarized manifolds and for polarized manifolds with a semi-ample canonical sheaf.

Author : Frank W. Warner
Publisher : Springer Science & Business Media
Page : 283 pages
File Size : 51,7 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.

Author : Jet Nestruev
Publisher : Springer Nature
Page : 433 pages
File Size : 49,6 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.

Author : Fangyang Zheng
Publisher : American Mathematical Soc.
Page : 275 pages
File Size : 48,9 Mb
Release : 2000
Category : Complex manifolds
ISBN : 9780821829608

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Complex Differential Geometry by Fangyang Zheng Pdf

Discusses the differential geometric aspects of complex manifolds. This work contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. It discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles. It also gives a brief account of the surface classification theory.

Author : Shiing-shen Chern
Publisher : Springer Science & Business Media
Page : 158 pages
File Size : 42,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781468493443

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Complex Manifolds without Potential Theory by Shiing-shen Chern Pdf

From the reviews of the second edition: "The new methods of complex manifold theory are very useful tools for investigations in algebraic geometry, complex function theory, differential operators and so on. The differential geometrical methods of this theory were developed essentially under the influence of Professor S.-S. Chern's works. The present book is a second edition... It can serve as an introduction to, and a survey of, this theory and is based on the author's lectures held at the University of California and at a summer seminar of the Canadian Mathematical Congress.... The text is illustrated by many examples... The book is warmly recommended to everyone interested in complex differential geometry." #Acta Scientiarum Mathematicarum, 41, 3-4#

Author : Izu Vaisman
Publisher : Courier Dover Publications
Page : 304 pages
File Size : 53,9 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.

Author : Mark Goresky,Robert MacPherson
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 46,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642717147

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Stratified Morse Theory by Mark Goresky,Robert MacPherson Pdf

Due to the lack of proper bibliographical sources stratification theory seems to be a "mysterious" subject in contemporary mathematics. This book contains a complete and elementary survey - including an extended bibliography - on stratification theory, including its historical development. Some further important topics in the book are: Morse theory, singularities, transversality theory, complex analytic varieties, Lefschetz theorems, connectivity theorems, intersection homology, complements of affine subspaces and combinatorics. The book is designed for all interested students or professionals in this area.

Author : Friedrich Hirzebruch
Publisher : Springer
Page : 241 pages
File Size : 51,9 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9783662306970

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Topological Methods in Algebraic Geometry by Friedrich Hirzebruch Pdf