Cohomological Methods In Homotopy Theory

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Cohomological Methods in Homotopy Theory

Jaume Aguade,Carles Broto,Carles Casacuberta
Cohomological Methods in Homotopy Theory Book PDF

Author : Jaume Aguade,Carles Broto,Carles Casacuberta
Publisher : Birkhäuser
Page : 413 pages
File Size : 52,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034883122

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Cohomological Methods in Homotopy Theory by Jaume Aguade,Carles Broto,Carles Casacuberta Pdf

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

J. Aguadé,Carles Broto,Carlos Casacuberta
Cohomological Methods in Homotopy Theory Book PDF

Author : J. Aguadé,Carles Broto,Carlos Casacuberta
Publisher : Birkhauser
Page : 415 pages
File Size : 47,8 Mb
Release : 2001-01-01
Category : Mathematics
ISBN : 0817665889

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Cohomological Methods in Homotopy Theory by J. Aguadé,Carles Broto,Carlos Casacuberta Pdf

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

William G. Dwyer,Hans-Werner Henn
Homotopy Theoretic Methods in Group Cohomology Book PDF

Author : William G. Dwyer,Hans-Werner Henn
Publisher : Birkhäuser
Page : 106 pages
File Size : 48,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034883566

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Homotopy Theoretic Methods in Group Cohomology by William G. Dwyer,Hans-Werner Henn Pdf

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

C. Allday,V. Puppe
Cohomological Methods in Transformation Groups Book PDF

Author : C. Allday,V. Puppe
Publisher : Cambridge University Press
Page : 486 pages
File Size : 49,9 Mb
Release : 1993-07
Category : Mathematics
ISBN : 9780521350228

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Cohomological Methods in Transformation Groups by C. Allday,V. Puppe Pdf

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.

Cohomology Operations and Applications in Homotopy Theory

Robert E. Mosher,Martin C. Tangora
Cohomology Operations and Applications in Homotopy Theory Book PDF

Author : Robert E. Mosher,Martin C. Tangora
Publisher : Courier Corporation
Page : 226 pages
File Size : 51,7 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 9780486466644

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Cohomology Operations and Applications in Homotopy Theory by Robert E. Mosher,Martin C. Tangora Pdf

Cohomology operations are at the center of a major area of activity in algebraic topology. This treatment explores the single most important variety of operations, the Steenrod squares. It constructs these operations, proves their major properties, and provides numerous applications, including several different techniques of homotopy theory useful for computation. 1968 edition.

Algebraic Topology--homotopy and Homology

Robert M. Switzer
Algebraic Topology homotopy and Homology Book PDF

Author : Robert M. Switzer
Publisher : Springer
Page : 548 pages
File Size : 47,9 Mb
Release : 1975
Category : Mathematics
ISBN : UOM:39015016365895

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Algebraic Topology--homotopy and Homology by Robert M. Switzer Pdf

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 Theory: An Introduction to Algebraic Topology

Anonim
Homotopy Theory An Introduction to Algebraic Topology Book PDF

Author : Anonim
Publisher : Academic Press
Page : 367 pages
File Size : 55,6 Mb
Release : 1975-11-12
Category : Mathematics
ISBN : 0080873804

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Homotopy Theory: An Introduction to Algebraic Topology by Anonim Pdf

Homotopy Theory: An Introduction to Algebraic Topology

Homotopy of Operads and Grothendieck-Teichmuller Groups

Benoit Fresse
Homotopy of Operads and Grothendieck Teichmuller Groups Book PDF

Author : Benoit Fresse
Publisher : American Mathematical Soc.
Page : 704 pages
File Size : 40,9 Mb
Release : 2017-05-22
Category : Grothendieck groups
ISBN : 9781470434823

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Homotopy of Operads and Grothendieck-Teichmuller Groups by Benoit Fresse Pdf

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 and Arithmetic Geometry – Motivic and Diophantine Aspects

Frank Neumann,Ambrus Pál
Homotopy Theory and Arithmetic Geometry Motivic and Diophantine Aspects Book PDF

Author : Frank Neumann,Ambrus Pál
Publisher : Springer Nature
Page : 223 pages
File Size : 54,7 Mb
Release : 2021-09-29
Category : Mathematics
ISBN : 9783030789770

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Homotopy Theory and Arithmetic Geometry – Motivic and Diophantine Aspects by Frank Neumann,Ambrus Pál Pdf

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.

Parametrized Homotopy Theory

J. Peter May,Johann Sigurdsson
Parametrized Homotopy Theory Book PDF

Author : J. Peter May,Johann Sigurdsson
Publisher : American Mathematical Soc.
Page : 456 pages
File Size : 54,8 Mb
Release : 2006
Category : Homotopy equivalences
ISBN : 9780821839225

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Parametrized Homotopy Theory by J. Peter May,Johann Sigurdsson Pdf

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

John Patrick Campbell Greenlees,Robert Ray Bruner,Nicholas John Kuhn
Homotopy Methods in Algebraic Topology Book PDF

Author : John Patrick Campbell Greenlees,Robert Ray Bruner,Nicholas John Kuhn
Publisher : American Mathematical Soc.
Page : 374 pages
File Size : 41,6 Mb
Release : 2001
Category : Mathematics
ISBN : 0821856073

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Homotopy Methods in Algebraic Topology by John Patrick Campbell Greenlees,Robert Ray Bruner,Nicholas John Kuhn Pdf

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.

Simplicial Homotopy Theory

Paul G. Goerss,John F. Jardine
Simplicial Homotopy Theory Book PDF

Author : Paul G. Goerss,John F. Jardine
Publisher : Birkhäuser
Page : 520 pages
File Size : 49,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034887076

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Simplicial Homotopy Theory by Paul G. Goerss,John F. Jardine Pdf

Since the beginning of the modern era of algebraic topology, simplicial methods have been used systematically and effectively for both computation and basic theory. With the development of Quillen's concept of a closed model category and, in particular, a simplicial model category, this collection of methods has become the primary way to describe non-abelian homological algebra and to address homotopy-theoretical issues in a variety of fields, including algebraic K-theory. This book supplies a modern exposition of these ideas, emphasizing model category theoretical techniques. Discussed here are the homotopy theory of simplicial sets, and other basic topics such as simplicial groups, Postnikov towers, and bisimplicial sets. The more advanced material includes homotopy limits and colimits, localization with respect to a map and with respect to a homology theory, cosimplicial spaces, and homotopy coherence. Interspersed throughout are many results and ideas well-known to experts, but uncollected in the literature. Intended for second-year graduate students and beyond, this book introduces many of the basic tools of modern homotopy theory. An extensive background in topology is not assumed.

Homotopy Theory of Schemes

Fabien Morel
Homotopy Theory of Schemes Book PDF

Author : Fabien Morel
Publisher : American Mathematical Soc.
Page : 116 pages
File Size : 44,8 Mb
Release : 2006
Category : Mathematics
ISBN : 082183164X

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Homotopy Theory of Schemes by Fabien Morel Pdf

In this text, the author presents a general framework for applying the standard methods from homotopy theory to the category of smooth schemes over a reasonable base scheme $k$. He defines the homotopy category $h(\mathcal{E} k)$ of smooth $k$-schemes and shows that it plays the same role for smooth $k$-schemes as the classical homotopy category plays for differentiable varieties. It is shown that certain expected properties are satisfied, for example, concerning the algebraic$K$-theory of those schemes. In this way, advanced methods of algebraic topology become available in modern algebraic geometry.

Introduction to Homotopy Theory

Paul Selick
Introduction to Homotopy Theory Book PDF

Author : Paul Selick
Publisher : American Mathematical Soc.
Page : 220 pages
File Size : 55,7 Mb
Release : 2008
Category : Mathematics
ISBN : 0821844369

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Introduction to Homotopy Theory by Paul Selick Pdf

Offers a summary for students and non-specialists who are interested in learning the basics of algebraic topology. This book covers fibrations and cofibrations, Hurewicz and cellular approximation theorems, topics in classical homotopy theory, simplicial sets, fiber bundles, Hopf algebras, and generalized homology and cohomology operations.

Equivariant Homotopy and Cohomology Theory

J. Peter May,M. Cole
Equivariant Homotopy and Cohomology Theory Book PDF

Author : J. Peter May,M. Cole
Publisher : American Mathematical Soc.
Page : 384 pages
File Size : 43,5 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821803196

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Equivariant Homotopy and Cohomology Theory by J. Peter May,M. Cole Pdf

This volume introduces equivariant homotopy, homology, and cohomology theory, along with various related topics in modern algebraic topology. It explains the main ideas behind some of the most striking recent advances in the subject. The works begins with a development of the equivariant algebraic topology of spaces culminating in a discussion of the Sullivan conjecture that emphasizes its relationship with classical Smith theory. The book then introduces equivariant stable homotopy theory, the equivariant stable homotopy category, and the most important examples of equivariant cohomology theories. The basic machinery that is needed to make serious use of equivariant stable homotopy theory is presented next, along with discussions of the Segal conjecture and generalized Tate cohomology. Finally, the book gives an introduction to "brave new algebra", the study of point-set level algebraic structures on spectra and its equivariant applications. Emphasis is placed on equivariant complex cobordism, and related results on that topic are presented in detail.