A User S Guide To Spectral Sequences
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A User S Guide To Spectral Sequences
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Author : John McCleary
language : en
Publisher: Cambridge University Press
Release Date : 2001
A User S Guide To Spectral Sequences written by John McCleary and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
Spectral sequences are among the most elegant and powerful methods of computation in mathematics. This book describes some of the most important examples of spectral sequences and some of their most spectacular applications. The first part treats the algebraic foundations for this sort of homological algebra, starting from informal calculations. The heart of the text is an exposition of the classical examples from homotopy theory, with chapters on the Leray-Serre spectral sequence, the Eilenberg-Moore spectral sequence, the Adams spectral sequence, and, in this new edition, the Bockstein spectral sequence. The last part of the book treats applications throughout mathematics, including the theory of knots and links, algebraic geometry, differential geometry and algebra. This is an excellent reference for students and researchers in geometry, topology, and algebra.
A User S Guide To Spectral Sequences
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Author : John McCleary
language : en
Publisher: Cambridge University Press
Release Date : 2000-11-27
A User S Guide To Spectral Sequences written by John McCleary and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-11-27 with Mathematics categories.
Spectral sequences are among the most elegant and powerful methods of computation in mathematics. This book describes some of the most important examples of spectral sequences and some of their most spectacular applications. The first part treats the algebraic foundations for this sort of homological algebra, starting from informal calculations. The heart of the text is an exposition of the classical examples from homotopy theory, with chapters on the Leray-Serre spectral sequence, the Eilenberg-Moore spectral sequence, the Adams spectral sequence, and, in this new edition, the Bockstein spectral sequence. The last part of the book treats applications throughout mathematics, including the theory of knots and links, algebraic geometry, differential geometry and algebra. This is an excellent reference for students and researchers in geometry, topology, and algebra.
A User S Guide To Algebraic Topology
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Author : C. T. J. Dodson
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-01-31
A User S Guide To Algebraic Topology written by C. T. J. Dodson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-31 with Mathematics categories.
This book arose from courses taught by the authors, and is designed for both instructional and reference use during and after a first course in algebraic topology. It is a handbook for users who want to calculate, but whose main interests are in applications using the current literature, rather than in developing the theory. Typical areas of applications are differential geometry and theoretical physics. We start gently, with numerous pictures to illustrate the fundamental ideas and constructions in homotopy theory that are needed in later chapters. We show how to calculate homotopy groups, homology groups and cohomology rings of most of the major theories, exact homotopy sequences of fibrations, some important spectral sequences, and all the obstructions that we can compute from these. Our approach is to mix illustrative examples with those proofs that actually develop transferable calculational aids. We give extensive appendices with notes on background material, extensive tables of data, and a thorough index. Audience: Graduate students and professionals in mathematics and physics.
A Multiplicative Tate Spectral Sequence For Compact Lie Group Actions
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Author : Alice Hedenlund
language : en
Publisher: American Mathematical Society
Release Date : 2024-03-18
A Multiplicative Tate Spectral Sequence For Compact Lie Group Actions written by Alice Hedenlund and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-18 with Mathematics categories.
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Introduction To Stable Homotopy Theory
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Author : David Barnes
language : en
Publisher: Cambridge University Press
Release Date : 2020-03-26
Introduction To Stable Homotopy Theory written by David Barnes and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-26 with Mathematics categories.
A comprehensive introduction to stable homotopy theory for beginning graduate students, from motivating phenomena to current research.
Stable Homotopy And Generalised Homology
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Author : John Frank Adams
language : en
Publisher: University of Chicago Press
Release Date : 1974
Stable Homotopy And Generalised Homology written by John Frank Adams and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Mathematics categories.
J. Frank Adams, the founder of stable homotopy theory, gave a lecture series at the University of Chicago in 1967, 1970, and 1971, the well-written notes of which are published in this classic in algebraic topology. The three series focused on Novikov's work on operations in complex cobordism, Quillen's work on formal groups and complex cobordism, and stable homotopy and generalized homology. Adams's exposition of the first two topics played a vital role in setting the stage for modern work on periodicity phenomena in stable homotopy theory. His exposition on the third topic occupies the bulk of the book and gives his definitive treatment of the Adams spectral sequence along with many detailed examples and calculations in KU-theory that help give a feel for the subject.
Topology And Quantum Theory In Interaction
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Author : David Ayala
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-10-25
Topology And Quantum Theory In Interaction written by David Ayala and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-25 with Mathematics categories.
This volume contains the proceedings of the NSF-CBMS Regional Conference on Topological and Geometric Methods in QFT, held from July 31–August 4, 2017, at Montana State University in Bozeman, Montana. In recent decades, there has been a movement to axiomatize quantum field theory into a mathematical structure. In a different direction, one can ask to test these axiom systems against physics. Can they be used to rederive known facts about quantum theories or, better yet, be the framework in which to solve open problems? Recently, Freed and Hopkins have provided a solution to a classification problem in condensed matter theory, which is ultimately based on the field theory axioms of Graeme Segal. Papers contained in this volume amplify various aspects of the Freed–Hopkins program, develop some category theory, which lies behind the cobordism hypothesis, the major structure theorem for topological field theories, and relate to Costello's approach to perturbative quantum field theory. Two papers on the latter use this framework to recover fundamental results about some physical theories: two-dimensional sigma-models and the bosonic string. Perhaps it is surprising that such sparse axiom systems encode enough structure to prove important results in physics. These successes can be taken as encouragement that the axiom systems are at least on the right track toward articulating what a quantum field theory is.
Categorical Decomposition Techniques In Algebraic Topology
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Author : Gregory Arone
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Categorical Decomposition Techniques In Algebraic Topology written by Gregory Arone and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The book consists of articles at the frontier of current research in Algebraic Topology. It presents recent results by top notch experts, and is intended primarily for researchers and graduate students working in the field of algebraic topology. Included is an important article by Cohen, Johnes and Yan on the homology of the space of smooth loops on a manifold M, endowed with the Chas-Sullivan intersection product, as well as an article by Goerss, Henn and Mahowald on stable homotopy groups of spheres, which uses the cutting edge technology of "topological modular forms".
Differential Geometry
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Author : Elisabetta Barletta
language : en
Publisher: Springer Nature
Release Date : 2025-02-06
Differential Geometry written by Elisabetta Barletta and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-06 with Mathematics categories.
This book, Differential Geometry: Manifolds, Bundles and Characteristic Classes (Book I-A), is the first in a captivating series of four books presenting a choice of topics, among fundamental and more advanced, in differential geometry (DG), such as manifolds and tensor calculus, differentiable actions and principal bundles, parallel displacement and exponential mappings, holonomy, complex line bundles and characteristic classes. The inclusion of an appendix on a few elements of algebraic topology provides a didactical guide towards the more advanced Algebraic Topology literature. The subsequent three books of the series are: Differential Geometry: Riemannian Geometry and Isometric Immersions (Book I-B) Differential Geometry: Foundations of Cauchy-Riemann and Pseudohermitian Geometry (Book I-C) Differential Geometry: Advanced Topics in Cauchy–Riemann and Pseudohermitian Geometry (Book I-D) The four books belong to an ampler book project (Differential Geometry, Partial Differential Equations, and Mathematical Physics, by the same authors) and aim to demonstrate how certain portions of DG and the theory of partial differential equations apply to general relativity and (quantum) gravity theory. These books supply some of the ad hoc DG machinery yet do not constitute a comprehensive treatise on DG, but rather Authors’ choice based on their scientific (mathematical and physical) interests. These are centered around the theory of immersions - isometric, holomorphic, and Cauchy-Riemann (CR) -and pseudohermitian geometry, as devised by Sidney Martin Webster for the study of nondegenerate CR structures, themselves a DG manifestation of the tangential CR equations.
Spectral Spaces
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Author : Max Dickmann
language : en
Publisher: Cambridge University Press
Release Date : 2019-03-21
Spectral Spaces written by Max Dickmann and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-21 with Mathematics categories.
Offers a comprehensive presentation of spectral spaces focussing on their topology and close connections with algebra, ordered structures, and logic.