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| Author | : Daniel Rosiak |
| Publisher | : MIT Press |
| Total Pages | : 454 |
| Release | : 2022-10-25 |
| Genre | : Mathematics |
| ISBN | : 0262362376 |
Download Sheaf Theory through Examples Book in PDF, ePub and Kindle
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.
| Author | : Glen E. Bredon |
| Publisher | : |
| Total Pages | : 296 |
| Release | : 1967 |
| Genre | : Sheaf theory |
| ISBN | : |
Download Sheaf Theory Book in PDF, ePub and Kindle
| Author | : Masaki Kashiwara |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 536 |
| Release | : 2002-05-01 |
| Genre | : Mathematics |
| ISBN | : 9783540518617 |
Download Sheaves on Manifolds Book in PDF, ePub and Kindle
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 | : Masaki Kashiwara |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 496 |
| Release | : 2005-12-19 |
| Genre | : Mathematics |
| ISBN | : 3540279504 |
Download Categories and Sheaves Book in PDF, ePub and Kindle
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 | : Ryoshi Hotta |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 408 |
| Release | : 2007-11-07 |
| Genre | : Mathematics |
| ISBN | : 081764363X |
Download D-Modules, Perverse Sheaves, and Representation Theory Book in PDF, ePub and Kindle
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.
| Author | : B. R. Tennison |
| Publisher | : Cambridge University Press |
| Total Pages | : 177 |
| Release | : 1975-12-18 |
| Genre | : Mathematics |
| ISBN | : 0521207843 |
Download Sheaf Theory Book in PDF, ePub and Kindle
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.
| Author | : Glen E. Bredon |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 518 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461206472 |
Download Sheaf Theory Book in PDF, ePub and Kindle
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.
| Author | : S. Ramanan |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 330 |
| Release | : 2005 |
| Genre | : Mathematics |
| ISBN | : 0821837028 |
Download Global Calculus Book in PDF, ePub and Kindle
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 | : Torsten Wedhorn |
| Publisher | : Springer |
| Total Pages | : 366 |
| Release | : 2016-07-25 |
| Genre | : Mathematics |
| ISBN | : 3658106336 |
Download Manifolds, Sheaves, and Cohomology Book in PDF, ePub and Kindle
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 | : Birger Iversen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 476 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642827837 |
Download Cohomology of Sheaves Book in PDF, ePub and Kindle
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.
