Cohomological Methods In Homotopy Theory
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Cohomological Methods In Homotopy Theory
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Author : Jaume Aguade
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Cohomological Methods In Homotopy Theory written by Jaume Aguade 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.
This book contains a collection of articles summarizing the state of knowledge in a large portion of modern homotopy theory. A call for articles was made on the occasion of an emphasis semester organized by the Centre de Recerca Matemtica in Bellaterra (Barcelona) in 1998. The main topics treated in the book include abstract features of stable and unstable homotopy, homotopical localizations, p-compact groups, H-spaces, classifying spaces for proper actions, cohomology of discrete groups, K-theory and other generalized cohomology theories, configuration spaces, and Lusternik-Schnirelmann category. The book is addressed to all mathematicians interested in homotopy theory and in geometric aspects of group theory. New research directions in topology are highlighted. Moreover, this informative and educational book serves as a welcome reference for many new results and recent methods.
Cohomological Methods In Homotopy Theory
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Author : J. Aguadé
language : en
Publisher: Birkhauser
Release Date : 2001-01-01
Cohomological Methods In Homotopy Theory written by J. Aguadé and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Mathematics categories.
This book contains a collection of articles summarizing the state of knowledge in a large portion of modern homotopy theory. A call for articles was made on the occasion of an emphasis semester organized by the Centre de Recerca MatemA tica in Bellaterra (Barcelona) in 1998. The main topics treated in the book include abstract features of stable and unstable homotopy, homotopical localizations, p-compact groups, H-spaces, classifying spaces for proper actions, cohomology of discrete groups, K-theory and other generalized cohomology theories, configuration spaces, and Lusternik-Schnirelmann category.The book is addressed to all mathematicians interested in homotopy theory and in geometric aspects of group theory. New research directions in topology are highlighted. Moreover, this informative and educational book serves as a welcome reference for many new results and recent methods.
Homotopy Theoretic Methods In Group Cohomology
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Author : William G. Dwyer
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Homotopy Theoretic Methods In Group Cohomology written by William G. Dwyer 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.
This book consists essentially of notes which were written for an Advanced Course on Classifying Spaces and Cohomology of Groups. The course took place at the Centre de Recerca Mathematica (CRM) in Bellaterra from May 27 to June 2, 1998 and was part of an emphasis semester on Algebraic Topology. It consisted of two parallel series of 6 lectures of 90 minutes each and was intended as an introduction to new homotopy theoretic methods in group cohomology. The first part of the book is concerned with methods of decomposing the classifying space of a finite group into pieces made of classifying spaces of appropriate subgroups. Such decompositions have been used with great success in the last 10-15 years in the homotopy theory of classifying spaces of compact Lie groups and p-compact groups in the sense of Dwyer and Wilkerson. For simplicity the emphasis here is on finite groups and on homological properties of various decompositions known as centralizer resp. normalizer resp. subgroup decomposition. A unified treatment of the various decompositions is given and the relations between them are explored. This is preceeded by a detailed discussion of basic notions such as classifying spaces, simplicial complexes and homotopy colimits.
Cohomological Methods In Transformation Groups
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Author : C. Allday
language : en
Publisher: Cambridge University Press
Release Date : 1993-07
Cohomological Methods In Transformation Groups written by C. Allday 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 1993-07 with Mathematics categories.
This is an account of the theory of certain types of compact transformation groups, namely those that are susceptible to study using ordinary cohomology theory and rational homotopy theory, which in practice means the torus groups and elementary abelian p-groups. The efforts of many mathematicians have combined to bring a depth of understanding to this area. However to make it reasonably accessible to a wide audience, the authors have streamlined the presentation, referring the reader to the literature for purely technical results and working in a simplified setting where possible. In this way the reader with a relatively modest background in algebraic topology and homology theory can penetrate rather deeply into the subject, whilst the book at the same time makes a useful reference for the more specialised reader.
Homotopy Theory And Arithmetic Geometry Motivic And Diophantine Aspects
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Author : Frank Neumann
language : en
Publisher: Springer Nature
Release Date : 2021-09-29
Homotopy Theory And Arithmetic Geometry Motivic And Diophantine Aspects written by Frank Neumann and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-29 with Mathematics categories.
This book provides an introduction to state-of-the-art applications of homotopy theory to arithmetic geometry. The contributions to this volume are based on original lectures by leading researchers at the LMS-CMI Research School on ‘Homotopy Theory and Arithmetic Geometry - Motivic and Diophantine Aspects’ and the Nelder Fellow Lecturer Series, which both took place at Imperial College London in the summer of 2018. The contribution by Brazelton, based on the lectures by Wickelgren, provides an introduction to arithmetic enumerative geometry, the notes of Cisinski present motivic sheaves and new cohomological methods for intersection theory, and Schlank’s contribution gives an overview of the use of étale homotopy theory for obstructions to the existence of rational points on algebraic varieties. Finally, the article by Asok and Østvær, based in part on the Nelder Fellow lecture series by Østvær, gives a survey of the interplay between motivic homotopy theory and affine algebraic geometry, with a focus on contractible algebraic varieties. Now a major trend in arithmetic geometry, this volume offers a detailed guide to the fascinating circle of recent applications of homotopy theory to number theory. It will be invaluable to research students entering the field, as well as postdoctoral and more established researchers.
Algebraic Topology Homotopy And Homology
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Author : Robert M. Switzer
language : en
Publisher: Springer
Release Date : 1975
Algebraic Topology Homotopy And Homology written by Robert M. Switzer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Mathematics categories.
The author has attempted an ambitious and most commendable project. He assumes only a modest knowledge of algebraic topology on the part of the reader to start with, and he leads the reader systematically to the point at which he can begin to tackle problems in the current areas of research centered around generalized homology theories and their applications. After an account of classical homotopy theory, the author turns to homology and cohomology theories, first treating them axiomatically and then constructing them using spectra. These ideas are illustrated via a thorough development of the three main examples of ordinary homology, K-theory and bordisms. Next, the author takes up the study of products in homology and cohomology and the related questions of orientability and duality. The remainder of the book is devoted to more sophisticated techniques and methods currently in use such as characteristic classes, cohomology operations, and the Adams spectral sequence, all of which are developed in the context of generalized homology theories. This book is, all in all, a very admirable work and a valuable addition to the literature and its value is not diminished by the somewhat minor flaws mentioned. -- S.Y. Husseini.
Homotopy Of Operads And Grothendieck Teichmuller Groups
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Author : Benoit Fresse
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-05-22
Homotopy Of Operads And Grothendieck Teichmuller Groups written by Benoit Fresse 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 2017-05-22 with Grothendieck groups categories.
The ultimate goal of this book is to explain that the Grothendieck–Teichmüller group, as defined by Drinfeld in quantum group theory, has a topological interpretation as a group of homotopy automorphisms associated to the little 2-disc operad. To establish this result, the applications of methods of algebraic topology to operads must be developed. This volume is devoted primarily to this subject, with the main objective of developing a rational homotopy theory for operads. The book starts with a comprehensive review of the general theory of model categories and of general methods of homotopy theory. The definition of the Sullivan model for the rational homotopy of spaces is revisited, and the definition of models for the rational homotopy of operads is then explained. The applications of spectral sequence methods to compute homotopy automorphism spaces associated to operads are also explained. This approach is used to get a topological interpretation of the Grothendieck–Teichmüller group in the case of the little 2-disc operad. This volume is intended for graduate students and researchers interested in the applications of homotopy theory methods in operad theory. It is accessible to readers with a minimal background in classical algebraic topology and operad theory.
Homotopy Theory An Introduction To Algebraic Topology
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Author :
language : en
Publisher: Academic Press
Release Date : 1975-11-12
Homotopy Theory An Introduction To Algebraic Topology written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975-11-12 with Mathematics categories.
Homotopy Theory: An Introduction to Algebraic Topology
Parametrized Homotopy Theory
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Author : J. Peter May
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Parametrized Homotopy Theory written by J. Peter May 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 2006 with Homotopy equivalences categories.
This book develops rigorous foundations for parametrized homotopy theory, which is the algebraic topology of spaces and spectra that are continuously parametrized by the points of a base space. It also begins the systematic study of parametrized homology and cohomology theories. The parametrized world provides the natural home for many classical notions and results, such as orientation theory, the Thom isomorphism, Atiyah and Poincare duality, transfer maps, the Adams and Wirthmuller isomorphisms, and the Serre and Eilenberg-Moore spectral sequences. But in addition to providing a clearer conceptual outlook on these classical notions, it also provides powerful methods to study new phenomena, such as twisted $K$-theory, and to make new constructions, such as iterated Thom spectra. Duality theory in the parametrized setting is particularly illuminating and comes in two flavors. One allows the construction and analysis of transfer maps, and a quite different one relates parametrized homology to parametrized cohomology. The latter is based formally on a new theory of duality in symmetric bicategories that is of considerable independent interest. The text brings together many recent developments in homotopy theory. It provides a highly structured theory of parametrized spectra, and it extends parametrized homotopy theory to the equivariant setting. The theory of topological model categories is given a more thorough treatment than is available in the literature. This is used, together with an interesting blend of classical methods, to resolve basic foundational problems that have no nonparametrized counterparts.
Homotopy Methods In Algebraic Topology
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Author : John Patrick Campbell Greenlees
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Homotopy Methods In Algebraic Topology 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 2001 with Mathematics categories.
This volume presents the proceedings from the AMS-IMS-SIAM Summer Research Conference on Homotopy Methods in Algebraic Topology held at the University of Colorado.The conference coincided with the sixtieth birthday of J. Peter May. An article is included reflecting his wide-ranging and influential contributions to the subject area. Other articles in the book discuss the Adams $E 2$ term for elliptic cohomology, mapping class groups and function spaces, rational SO(3) equivariant cohomology theories, toral groups and classifying spaces of $p$-compact groups, dual calculus for functors to spectra, flatness for the $E {\infty}$ tensor product, and further related areas. The book offers a true comprehensive source on modern aspects of homotopy theoretic methods exported to algebraic settings.