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Sheaves In Topology
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Book Synopsis Sheaves in Topology by : Alexandru Dimca
Download or read book Sheaves in Topology written by Alexandru Dimca and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Topology of Singular Spaces and Constructible Sheaves by : Jörg Schürmann
Download or read book Topology of Singular Spaces and Constructible Sheaves written by Jörg Schürmann and published by Birkhäuser. This book was released on 2012-12-06 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Categories and Sheaves by : Masaki Kashiwara
Download or read book Categories and Sheaves written by Masaki Kashiwara and published by Springer Science & Business Media. This book was released on 2005-12-20 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Sheaf Theory through Examples by : Daniel Rosiak
Download or read book Sheaf Theory through Examples written by Daniel Rosiak and published by MIT Press. This book was released on 2022-10-25 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Sheaf Theory written by Glen E. Bredon and published by . This book was released on 1967 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Intersection Homology & Perverse Sheaves by : Laurenţiu G. Maxim
Download or read book Intersection Homology & Perverse Sheaves written by Laurenţiu G. Maxim and published by Springer Nature. This book was released on 2019-11-30 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Sheaves in Geometry and Logic by : Saunders Mac Lane
Download or read book Sheaves in Geometry and Logic written by Saunders Mac Lane and published by . This book was released on 1992 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the theory of toposes which begins with illustrative examples and goes on to explain the underlying ideas of topology and sheaf theory as well as the general theory of elementary toposes and geometric morphisms and their relation to logic.
Book Synopsis Sheaves on Manifolds by : Masaki Kashiwara
Download or read book Sheaves on Manifolds written by Masaki Kashiwara and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Manifolds, Sheaves, and Cohomology by : Torsten Wedhorn
Download or read book Manifolds, Sheaves, and Cohomology written by Torsten Wedhorn and published by Springer. This book was released on 2016-07-25 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Cohomology of Sheaves by : Birger Iversen
Download or read book Cohomology of Sheaves written by Birger Iversen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text exposes the basic features of cohomology of sheaves and its applications. The general theory of sheaves is very limited and no essential result is obtainable without turn ing to particular classes of topological spaces. The most satis factory general class is that of locally compact spaces and it is the study of such spaces which occupies the central part of this text. The fundamental concepts in the study of locally compact spaces is cohomology with compact support and a particular class of sheaves,the so-called soft sheaves. This class plays a double role as the basic vehicle for the internal theory and is the key to applications in analysis. The basic example of a soft sheaf is the sheaf of smooth functions on ~n or more generally on any smooth manifold. A rather large effort has been made to demon strate the relevance of sheaf theory in even the most elementary analysis. This process has been reversed in order to base the fundamental calculations in sheaf theory on elementary analysis.
Download or read book Global Calculus written by S. Ramanan and published by American Mathematical Soc.. This book was released on 2005 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A1-Algebraic Topology over a Field by : Fabien Morel
Download or read book A1-Algebraic Topology over a Field written by Fabien Morel and published by Springer. This book was released on 2012-07-13 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text deals with A1-homotopy theory over a base field, i.e., with the natural homotopy theory associated to the category of smooth varieties over a field in which the affine line is imposed to be contractible. It is a natural sequel to the foundational paper on A1-homotopy theory written together with V. Voevodsky. Inspired by classical results in algebraic topology, we present new techniques, new results and applications related to the properties and computations of A1-homotopy sheaves, A1-homology sheaves, and sheaves with generalized transfers, as well as to algebraic vector bundles over affine smooth varieties.
Book Synopsis Perverse Sheaves and Applications to Representation Theory by : Pramod N. Achar
Download or read book Perverse Sheaves and Applications to Representation Theory written by Pramod N. Achar and published by American Mathematical Soc.. This book was released on 2021-09-27 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its inception around 1980, the theory of perverse sheaves has been a vital tool of fundamental importance in geometric representation theory. This book, which aims to make this theory accessible to students and researchers, is divided into two parts. The first six chapters give a comprehensive account of constructible and perverse sheaves on complex algebraic varieties, including such topics as Artin's vanishing theorem, smooth descent, and the nearby cycles functor. This part of the book also has a chapter on the equivariant derived category, and brief surveys of side topics including étale and ℓ-adic sheaves, D-modules, and algebraic stacks. The last four chapters of the book show how to put this machinery to work in the context of selected topics in geometric representation theory: Kazhdan-Lusztig theory; Springer theory; the geometric Satake equivalence; and canonical bases for quantum groups. Recent developments such as the p-canonical basis are also discussed. The book has more than 250 exercises, many of which focus on explicit calculations with concrete examples. It also features a 4-page “Quick Reference” that summarizes the most commonly used facts for computations, similar to a table of integrals in a calculus textbook.
Book Synopsis Geometry of Vector Sheaves by : Anastasios Mallios
Download or read book Geometry of Vector Sheaves written by Anastasios Mallios and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Geometry of Moduli Spaces of Sheaves by : Daniel Huybrechts
Download or read book The Geometry of Moduli Spaces of Sheaves written by Daniel Huybrechts and published by Cambridge University Press. This book was released on 2010-05-27 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.
Book Synopsis Homology, Cohomology, and Sheaf Cohomology for Algebraic Topology, Algebraic Geometry, and Differential Geometry by : Jean H. Gallier
Download or read book Homology, Cohomology, and Sheaf Cohomology for Algebraic Topology, Algebraic Geometry, and Differential Geometry written by Jean H. Gallier and published by World Scientific Publishing Company. This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homology and cohomology -- De Rham cohomology -- Singular homology and cohomology -- Simplicial homology and cohomology -- Homology and cohomology of CW complexes -- Poincaré duality -- Presheaves and sheaves; Basics -- Cech cohomology with values in a presheaf -- Presheaves and sheaves; A deeper look -- Derived functors, [delta]-functors, and [del]-functors -- Universal coefficient theorems -- Cohomology of sheaves -- Alexander and Alexander-Lefschetz duality -- Spectral sequences.
Book Synopsis D-Modules, Perverse Sheaves, and Representation Theory by : Ryoshi Hotta
Download or read book D-Modules, Perverse Sheaves, and Representation Theory written by Ryoshi Hotta and published by Springer Science & Business Media. This book was released on 2007-11-07 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
