Sheaf Theory Through Examples PDF Download
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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 | : Alexandru Dimca |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 253 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642188680 |
Download Sheaves in Topology Book in PDF, ePub and Kindle
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 | : Eberhard Freitag |
| Publisher | : Createspace Independent Publishing Platform |
| Total Pages | : 0 |
| Release | : 2014-09-22 |
| Genre | : Riemann surfaces |
| ISBN | : 9781500983666 |
Download Riemann Surfaces Book in PDF, ePub and Kindle
The book contains an introduction into the theory of Riemann surfaces using a sheaf theoretic approach. Sheaf theory is developed completely. The cohomology of sheaves is introduced by means of the canonical flabby resolution of Godement. The Riemann-Roch theorem is proved for vector bundles. Abel's theorem and the Jacobi inversion theorem are treated. As application, dimension formulae for vector valued automorphic forms in one variable are proved. The necessary tools from topology and algebra are described completely but highly focussed.
| Author | : Michael Robinson |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 245 |
| Release | : 2014-01-07 |
| Genre | : Technology & Engineering |
| ISBN | : 3642361048 |
Download Topological Signal Processing Book in PDF, ePub and Kindle
Signal processing is the discipline of extracting information from collections of measurements. To be effective, the measurements must be organized and then filtered, detected, or transformed to expose the desired information. Distortions caused by uncertainty, noise, and clutter degrade the performance of practical signal processing systems. In aggressively uncertain situations, the full truth about an underlying signal cannot be known. This book develops the theory and practice of signal processing systems for these situations that extract useful, qualitative information using the mathematics of topology -- the study of spaces under continuous transformations. Since the collection of continuous transformations is large and varied, tools which are topologically-motivated are automatically insensitive to substantial distortion. The target audience comprises practitioners as well as researchers, but the book may also be beneficial for graduate students.
| 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 | : 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 | : 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 | : Kenji Ueno |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 196 |
| Release | : 1999 |
| Genre | : Mathematics |
| ISBN | : 9780821813577 |
Download Algebraic Geometry 2 Book in PDF, ePub and Kindle
Algebraic geometry is built upon two fundamental notions: schemes and sheaves. The theory of schemes was explained in Algebraic Geometry 1: From Algebraic Varieties to Schemes. In this volume, the author turns to the theory of sheaves and their cohomology. A sheaf is a way of keeping track of local information defined on a topological space, such as the local holomorphic functions on a complex manifold or the local sections of a vector bundle. To study schemes, it is useful to study the sheaves defined on them, especially the coherent and quasicoherent sheaves.
| Author | : Pramod N. Achar |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 562 |
| Release | : 2021-09-27 |
| Genre | : Education |
| ISBN | : 1470455978 |
Download Perverse Sheaves and Applications to Representation Theory Book in PDF, ePub and Kindle
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.
