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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 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.
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 Bringing in the Sheaves: Transforming Poverty Into Productivity by :
Download or read book Bringing in the Sheaves: Transforming Poverty Into Productivity written by and published by . This book was released on 1996 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The Institute for Christian Economics (ICE) in Tyler, Texas, presents the full-text of "Bringing in the Sheaves: Transforming Poverty Into Productivity," as part of the ICE FreeBooks resource. The book, written by George Grant, was originally published in 1985, and is available online in HTML or PDF format. The book discusses the role of the church in reducing poverty.
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 Geometry of Principal Sheaves by : Efstathios Vassiliou
Download or read book Geometry of Principal Sheaves written by Efstathios Vassiliou and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a detailed introduction to the theory of connections on principal sheaves in the framework of Abstract Differential Geometry (ADG). This is a new approach to differential geometry based on sheaf theoretic methods, without use of ordinary calculus. This point of view complies with the demand of contemporary physics to cope with non-smooth models of physical phenomena and spaces with singularities. Starting with a brief survey of the required sheaf theory and cohomology, the exposition then moves on to differential triads (the abstraction of smooth manifolds) and Lie sheaves of groups (the abstraction of Lie groups). Having laid the groundwork, the main part of the book is devoted to the theory of connections on principal sheaves, incorporating connections on vector and associated sheaves. Topics such as the moduli sheaf of connections, classification of principal sheaves, curvature, flat connections and flat sheaves, Chern-Weil theory, are also treated. The study brings to light fundamental notions and tools of the standard differential geometry which are susceptible of the present abstraction, and whose role remains unexploited in the classical context, because of the abundance of means therein. However, most of the latter are nonsensical in ADG.
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 Algebraic Cycles, Sheaves, Shtukas, and Moduli by : Piotr Pragacz
Download or read book Algebraic Cycles, Sheaves, Shtukas, and Moduli written by Piotr Pragacz and published by Springer Science & Business Media. This book was released on 2008-03-12 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Articles examine the contributions of the great mathematician J. M. Hoene-Wronski. Although much of his work was dismissed during his lifetime, it is now recognized that his work offers valuable insight into the nature of mathematics. The book begins with elementary-level discussions and ends with discussions of current research. Most of the material has never been published before, offering fresh perspectives on Hoene-Wronski’s contributions.
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 of Algebras over Boolean Spaces by : Arthur Knoebel
Download or read book Sheaves of Algebras over Boolean Spaces written by Arthur Knoebel and published by Springer Science & Business Media. This book was released on 2011-12-15 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique monograph building bridges among a number of different areas of mathematics such as algebra, topology, and category theory. The author uses various tools to develop new applications of classical concepts. Detailed proofs are given for all major theorems, about half of which are completely new. Sheaves of Algebras over Boolean Spaces will take readers on a journey through sheaf theory, an important part of universal algebra. This excellent reference text is suitable for graduate students, researchers, and those who wish to learn about sheaves of algebras.
Book Synopsis D-Modules, Perverse Sheaves, and Representation Theory by : Kiyoshi Takeuchi
Download or read book D-Modules, Perverse Sheaves, and Representation Theory written by Kiyoshi Takeuchi and published by Springer Science & Business Media. This book was released on 2007-10-12 with total page 412 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.
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.
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 Invariant Differential Operators and the Cohomology of Lie Algebra Sheaves by : Franz W. Kamber
Download or read book Invariant Differential Operators and the Cohomology of Lie Algebra Sheaves written by Franz W. Kamber and published by American Mathematical Soc.. This book was released on 1971 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Exact Categories and Categories of Sheaves by : M. Barr
Download or read book Exact Categories and Categories of Sheaves written by M. Barr and published by Springer. This book was released on 2006-11-15 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Equivariant Sheaves and Functors by : Joseph Bernstein
Download or read book Equivariant Sheaves and Functors written by Joseph Bernstein and published by Springer. This book was released on 2006-11-15 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: The equivariant derived category of sheaves is introduced. All usual functors on sheaves are extended to the equivariant situation. Some applications to the equivariant intersection cohomology are given. The theory may be useful to specialists in representation theory, algebraic geometry or topology.
Book Synopsis Spectral Decompositions and Analytic Sheaves by : Jörg Eschmeier
Download or read book Spectral Decompositions and Analytic Sheaves written by Jörg Eschmeier and published by Oxford University Press. This book was released on 1996 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rapid developments in multivariable spectral theory have led to important and fascinating results which also have applications in other mathematical disciplines. In this book, various concepts from function theory and complex analytic geometry are drawn together to give a new approach to concrete spectral computations and give insights into new developments in the spectral theory of linear operators. Classical results from cohomology theory of Banach algebras, multidimensional spectral theory, and complex analytic geometry have been freshly interpreted using the language of homological algebra. The advantages of this approach are illustrated by a variety of examples, unexpected applications, and conceptually new ideas that should stimulate further research among mathematicians.
