Implications In Morava K Theory

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Implications In Morava K Theory

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Author : Richard M. Kane
language : en
Publisher: American Mathematical Soc.
Release Date : 1986

Implications In Morava K Theory written by Richard M. Kane 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 1986 with Mathematics categories.

This paper studies the mod 2 cohomology [italic]H*[italic]X of finite [italic]H-spaces. It is shown that when [italic]X is connected and simply connected then [italic]H*[italic]X has no indecomposables of even degree. As a consequence, [italic]H*([capital Greek]Omega[italic]X;[bold]Z) and [italic]K*[italic]X have no 2 torsion. The main result is proved by using Morava [script]K-theory.

Algebraic Topology Poznan 1989

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Author : Stefan Jackowski
language : en
Publisher: Springer
Release Date : 2006-11-14

Algebraic Topology Poznan 1989 written by Stefan Jackowski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

As part of the scientific activity in connection with the 70th birthday of the Adam Mickiewicz University in Poznan, an international conference on algebraic topology was held. In the resulting proceedings volume, the emphasis is on substantial survey papers, some presented at the conference, some written subsequently.

Secondary Cohomology Operations

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Author : John R. Harper
language : en
Publisher: American Mathematical Soc.
Release Date : 2002

Secondary Cohomology Operations written by John R. Harper 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 2002 with Mathematics categories.

Although the theory and applications of secondary cohomology operations are an important part of an advanced graduate-level algebraic topology course, there are few books on the subject. The AMS now fills that gap with the publication of the present volume. The author's main purpose in this book is to develop the theory of secondary cohomology operations for singular cohomology theory, which is treated in terms of elementary constructions from general homotopy theory. Among manyapplications considered are the Hopf invariant one theorem (for all primes $p$, including $p = 2$), Browder's theorem on higher Bockstein operations, and cohomology theory of Massey-Peterson fibrations. Numerous examples and exercises help readers to gain a working knowledge of the theory. A summary ofmore advanced parts of the core material is included in the first chapter. Prerequisite is basic algebraic topology, including the Steenrod operations. The book is geared toward graduate students and research mathematicians interested in algebraic topology and can be used for self-study or as a textbook for an advanced course on the topic. It is available in both hardcover and softcover editions.

Recent Progress In Homotopy Theory

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Author : Donald M. Davis
language : en
Publisher: American Mathematical Soc.
Release Date : 2002

Recent Progress In Homotopy Theory written by Donald M. Davis 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 2002 with Mathematics categories.

This volume presents the proceedings from the month-long program held at Johns Hopkins University (Baltimore, MD) on homotopy theory, sponsored by the Japan-U.S. Mathematics Institute (JAMI). The book begins with historical accounts on the work of Professors Peter Landweber and Stewart Priddy. Central among the other topics are the following: 1. classical and nonclassical theory of $H$-spaces, compact groups, and finite groups, 2. classical and chromatic homotopy theory andlocalization, 3. classical and topological Hochschild cohomology, 4. elliptic cohomology and its relation to Moonshine and topological modular forms, and 5. motivic cohomology and Chow rings. This volume surveys the current state of research in these areas and offers an overview of futuredirections.

A Classification Theorem For Homotopy Commutative H Spaces With Finitely Generated Bmod 2 Cohomology Rings

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Author : Michael Slack
language : en
Publisher: American Mathematical Soc.
Release Date : 1991

A Classification Theorem For Homotopy Commutative H Spaces With Finitely Generated Bmod 2 Cohomology Rings written by Michael Slack 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 1991 with Mathematics categories.

Many homological properties of Lie groups are derived strictly from homotopy-theoretic considerations and do not depend on any geometric or analytic structure. An H-space is a topological space having a continuous multiplication with unit. Generalizing from Lie group theory, John Hubbuck proved that a connected, homotopy commutative H-space which is a finite cell complex has the homotopy type of a torus. There are many interesting examples of H-spaces which are not finite complexes - loop spaces are one example. The aim of this book is to prove a version of Hubbuck's theorem in which the condition that the H-space be a finite cell complex is replaced by the condition that it have a finitely-generated mod 2 cohomology ring. The conclusion of the theorem is slightly more general in this case, and some mild associativity hypotheses are required. The method of proof uses established techniques in H-space theory, as well as a new obstruction-theoretic approach to (Araki-Kudo-Dyer-Lashof) homology operations for iterated loop spaces.

Steenrod Connections And Connectivity In H Spaces

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Author : James P. Lin
language : en
Publisher: American Mathematical Soc.
Release Date : 1987

Steenrod Connections And Connectivity In H Spaces written by James P. Lin 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 1987 with Mathematics categories.

Encyclopaedia Of Mathematics

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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Encyclopaedia Of Mathematics written by Michiel Hazewinkel 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 2012-12-06 with Mathematics categories.

This is the first Supplementary volume to Kluwer's highly acclaimed Encyclopaedia of Mathematics. This additional volume contains nearly 600 new entries written by experts and covers developments and topics not included in the already published 10-volume set. These entries have been arranged alphabetically throughout. A detailed index is included in the book. This Supplementary volume enhances the existing 10-volume set. Together, these eleven volumes represent the most authoritative, comprehensive up-to-date Encyclopaedia of Mathematics available.

Mathematical Reviews

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Author :
language : en
Publisher:
Release Date : 2006

Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.

Bousfield Classes And Ohkawa S Theorem

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Author : Takeo Ohsawa
language : en
Publisher: Springer Nature
Release Date : 2020-03-18

Bousfield Classes And Ohkawa S Theorem written by Takeo Ohsawa and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-18 with Mathematics categories.

This volume originated in the workshop held at Nagoya University, August 28–30, 2015, focusing on the surprising and mysterious Ohkawa's theorem: the Bousfield classes in the stable homotopy category SH form a set. An inspiring, extensive mathematical story can be narrated starting with Ohkawa's theorem, evolving naturally with a chain of motivational questions: Ohkawa's theorem states that the Bousfield classes of the stable homotopy category SH surprisingly forms a set, which is still very mysterious. Are there any toy models where analogous Bousfield classes form a set with a clear meaning? The fundamental theorem of Hopkins, Neeman, Thomason, and others states that the analogue of the Bousfield classes in the derived category of quasi-coherent sheaves Dqc(X) form a set with a clear algebro-geometric description. However, Hopkins was actually motivated not by Ohkawa's theorem but by his own theorem with Smith in the triangulated subcategory SHc, consisting of compact objects in SH. Now the following questions naturally occur: (1) Having theorems of Ohkawa and Hopkins-Smith in SH, are there analogues for the Morel-Voevodsky A1-stable homotopy category SH(k), which subsumes SH when k is a subfield of C?, (2) Was it not natural for Hopkins to have considered Dqc(X)c instead of Dqc(X)? However, whereas there is a conceptually simple algebro-geometrical interpretation Dqc(X)c = Dperf(X), it is its close relative Dbcoh(X) that traditionally, ever since Oka and Cartan, has been intensively studied because of its rich geometric and physical information. This book contains developments for the rest of the story and much more, including the chromatics homotopy theory, which the Hopkins–Smith theorem is based upon, and applications of Lurie's higher algebra, all by distinguished contributors.

The Homology Of Hopf Spaces

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Author : R.M. Kane
language : en
Publisher: North Holland
Release Date : 1988-08

The Homology Of Hopf Spaces written by R.M. Kane and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-08 with Mathematics categories.

This exposition of the theory of finite Hopf spaces details the development of the subject over the last thirty years, with the homology of such spaces as its main theme. The three chief areas of study in the volume are: - The study of finite H-spaces with torsion free integral homology. - The study of finite H-spaces with homology torsion. - The construction of finite H-spaces.