Rational Homotopy Theory Draft Version 96 2
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Rational Homotopy Theory Draft Version 96 2
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Author : Steve Halperin
language : en
Publisher:
Release Date : 1996
Rational Homotopy Theory Draft Version 96 2 written by Steve Halperin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.
Rational Homotopy Theory Ii
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Author : Yves Félix
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 2015
Rational Homotopy Theory Ii written by Yves Félix and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Mathematics categories.
Sequel to Rational homotopy theory (2001), but self contained--Introduction, following table of contents.
Rational S 1 Equivariant Stable Homotopy Theory
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Author : John Patrick Campbell Greenlees
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Rational S 1 Equivariant Stable Homotopy Theory written by John Patrick Campbell Greenlees 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 1999 with Mathematics categories.
The memoir presents a systematic study of rational S1-equivariant cohomology theories, and a complete algebraic model for them. It provides a classification of such cohomology theories in simple algebraic terms and a practical means of calculation. The power of the model is illustrated by analysis of the Segal conjecture, the behaviour of the Atiyah-Hirzebruch spectral sequence, the structure of S1-equivariant K-theory, and the rational behaviour of cyclotomic spectra and the topological cyclic homology construction.
From Categories To Homotopy Theory
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Author : Birgit Richter
language : en
Publisher: Cambridge University Press
Release Date : 2020-04-16
From Categories To Homotopy Theory written by Birgit Richter 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 2020-04-16 with Mathematics categories.
Bridge the gap between category theory and its applications in homotopy theory with this guide for graduate students and researchers.
Nilpotence And Periodicity In Stable Homotopy Theory
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Author : Douglas C. Ravenel
language : en
Publisher: Princeton University Press
Release Date : 1992-11-08
Nilpotence And Periodicity In Stable Homotopy Theory written by Douglas C. Ravenel and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-11-08 with Mathematics categories.
Nilpotence and Periodicity in Stable Homotopy Theory describes some major advances made in algebraic topology in recent years, centering on the nilpotence and periodicity theorems, which were conjectured by the author in 1977 and proved by Devinatz, Hopkins, and Smith in 1985. During the last ten years a number of significant advances have been made in homotopy theory, and this book fills a real need for an up-to-date text on that topic. Ravenel's first few chapters are written with a general mathematical audience in mind. They survey both the ideas that lead up to the theorems and their applications to homotopy theory. The book begins with some elementary concepts of homotopy theory that are needed to state the problem. This includes such notions as homotopy, homotopy equivalence, CW-complex, and suspension. Next the machinery of complex cobordism, Morava K-theory, and formal group laws in characteristic p are introduced. The latter portion of the book provides specialists with a coherent and rigorous account of the proofs. It includes hitherto unpublished material on the smash product and chromatic convergence theorems and on modular representations of the symmetric group.
Rings Modules And Algebras In Stable Homotopy Theory
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Author : Anthony D. Elmendorf
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Rings Modules And Algebras In Stable Homotopy Theory written by Anthony D. Elmendorf 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 1997 with Mathematics categories.
This book introduces a new point-set level approach to stable homotopy theory that has already had many applications and promises to have a lasting impact on the subject. Given the sphere spectrum $S$, the authors construct an associative, commutative, and unital smash product in a complete and cocomplete category of ``$S$-modules'' whose derived category is equivalent to the classical stable homotopy category. This construction allows for a simple and algebraically manageable definition of ``$S$-algebras'' and ``commutative $S$-algebras'' in terms of associative, or associative and commutative, products $R\wedge SR \longrightarrow R$. These notions are essentially equivalent to the earlier notions of $A {\infty $ and $E {\infty $ ring spectra, and the older notions feed naturally into the new framework to provide plentiful examples. There is an equally simple definition of $R$-modules in terms of maps $R\wedge SM\longrightarrow M$. When $R$ is commutative, the category of $R$-modules also has a
Algebraic Operads
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Author : Jean-Louis Loday
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-08
Algebraic Operads written by Jean-Louis Loday 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 2012-08-08 with Mathematics categories.
In many areas of mathematics some “higher operations” are arising. These havebecome so important that several research projects refer to such expressions. Higher operationsform new types of algebras. The key to understanding and comparing them, to creating invariants of their action is operad theory. This is a point of view that is 40 years old in algebraic topology, but the new trend is its appearance in several other areas, such as algebraic geometry, mathematical physics, differential geometry, and combinatorics. The present volume is the first comprehensive and systematic approach to algebraic operads. An operad is an algebraic device that serves to study all kinds of algebras (associative, commutative, Lie, Poisson, A-infinity, etc.) from a conceptual point of view. The book presents this topic with an emphasis on Koszul duality theory. After a modern treatment of Koszul duality for associative algebras, the theory is extended to operads. Applications to homotopy algebra are given, for instance the Homotopy Transfer Theorem. Although the necessary notions of algebra are recalled, readers are expected to be familiar with elementary homological algebra. Each chapter ends with a helpful summary and exercises. A full chapter is devoted to examples, and numerous figures are included. After a low-level chapter on Algebra, accessible to (advanced) undergraduate students, the level increases gradually through the book. However, the authors have done their best to make it suitable for graduate students: three appendices review the basic results needed in order to understand the various chapters. Since higher algebra is becoming essential in several research areas like deformation theory, algebraic geometry, representation theory, differential geometry, algebraic combinatorics, and mathematical physics, the book can also be used as a reference work by researchers.
Algebraic Topology
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Author : Allen Hatcher
language : en
Publisher: Cambridge University Press
Release Date : 2002
Algebraic Topology written by Allen Hatcher 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 2002 with Mathematics categories.
An introductory textbook suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises.
Topological Modular Forms
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Author : Christopher L. Douglas
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-12-04
Topological Modular Forms written by Christopher L. Douglas 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 2014-12-04 with Mathematics categories.
The theory of topological modular forms is an intricate blend of classical algebraic modular forms and stable homotopy groups of spheres. The construction of this theory combines an algebro-geometric perspective on elliptic curves over finite fields with techniques from algebraic topology, particularly stable homotopy theory. It has applications to and connections with manifold topology, number theory, and string theory. This book provides a careful, accessible introduction to topological modular forms. After a brief history and an extended overview of the subject, the book proper commences with an exposition of classical aspects of elliptic cohomology, including background material on elliptic curves and modular forms, a description of the moduli stack of elliptic curves, an explanation of the exact functor theorem for constructing cohomology theories, and an exploration of sheaves in stable homotopy theory. There follows a treatment of more specialized topics, including localization of spectra, the deformation theory of formal groups, and Goerss-Hopkins obstruction theory for multiplicative structures on spectra. The book then proceeds to more advanced material, including discussions of the string orientation, the sheaf of spectra on the moduli stack of elliptic curves, the homotopy of topological modular forms, and an extensive account of the construction of the spectrum of topological modular forms. The book concludes with the three original, pioneering and enormously influential manuscripts on the subject, by Hopkins, Miller, and Mahowald.
Proceedings Of The Glasgow Mathematical Association
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Author :
language : en
Publisher:
Release Date : 1961
Proceedings Of The Glasgow Mathematical Association written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Mathematics categories.