The Homology of Hopf Spaces PDF Download
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Author: R.M. Kane
Publisher: North Holland
ISBN:
Category : Mathematics
Languages : en
Pages : 504
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Book Description
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.
Author: R.M. Kane
Publisher: North Holland
ISBN:
Category : Mathematics
Languages : en
Pages : 504
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Book Description
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.
Author: Sergei S. Akbarov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110780917
Category : Mathematics
Languages : en
Pages : 794
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Book Description
The term "stereotype space" was introduced in 1995 and is used for a category of locally convex spaces with surprisingly elegant properties. In particular, it consists of spaces reflexive in the sense of Pontryagin, and at the same time it is very wide, since it contains all Fréchet spaces. Its study gives an unexpected point of view on functional analysis that brings this field closer to other main branches of mathematics, namely, to algebra and geometry.
Author: Akira Kōno
Publisher: American Mathematical Soc.
ISBN: 9780821835142
Category : Mathematics
Languages : en
Pages : 276
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Book Description
Aims to give an exposition of generalized (co)homology theories that can be read by a group of mathematicians who are not experts in algebraic topology. This title starts with basic notions of homotopy theory, and introduces the axioms of generalized (co)homology theory. It also discusses various types of generalized cohomology theories.
Author: Matilde Marcolli
Publisher: Springer Science & Business Media
ISBN: 3834898317
Category : Mathematics
Languages : en
Pages : 247
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Book Description
This book is aimed at presenting different methods and perspectives in the theory of Quantum Groups, bridging between the algebraic, representation theoretic, analytic, and differential-geometric approaches. It also covers recent developments in Noncommutative Geometry, which have close relations to quantization and quantum group symmetries. The volume collects surveys by experts which originate from an acitvity at the Max-Planck-Institute for Mathematics in Bonn.
Author: V. M. Buchstaber
Publisher: American Mathematical Soc.
ISBN: 1470418711
Category : Mathematics
Languages : en
Pages : 408
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Book Description
Articles in this collection are devoted to modern problems of topology, geometry, mathematical physics, and integrable systems, and they are based on talks given at the famous Novikov's seminar at the Steklov Institute of Mathematics in Moscow in 2012-2014. The articles cover many aspects of seemingly unrelated areas of modern mathematics and mathematical physics; they reflect the main scientific interests of the organizer of the seminar, Sergey Petrovich Novikov. The volume is suitable for graduate students and researchers interested in the corresponding areas of mathematics and physics.
Author: Michael Charles Crabb
Publisher: Springer Science & Business Media
ISBN: 1447112652
Category : Mathematics
Languages : en
Pages : 344
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Book Description
Topology occupies a central position in modern mathematics, and the concept of the fibre bundle provides an appropriate framework for studying differential geometry. Fibrewise homotopy theory is a very large subject that has attracted a good deal of research in recent years. This book provides an overview of the subject as it stands at present.
Author: Yves Félix
Publisher: American Mathematical Soc.
ISBN: 0821849298
Category : Mathematics
Languages : en
Pages : 246
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Book Description
This volume contains the proceedings of the Workshop on Homotopy Theory of Function Spaces and Related Topics, which was held at the Mathematisches Forschungsinstitut Oberwolfach, in Germany, from April 5-11, 2009. This volume contains fourteen original research articles covering a broad range of topics that include: localization and rational homotopy theory, evaluation subgroups, free loop spaces, Whitehead products, spaces of algebraic maps, gauge groups, loop groups, operads, and string topology. In addition to reporting on various topics in the area, this volume is supposed to facilitate the exchange of ideas within Homotopy Theory of Function Spaces, and promote cross-fertilization between Homotopy Theory of Function Spaces and other areas. With these latter aims in mind, this volume includes a survey article which, with its extensive bibliography, should help bring researchers and graduate students up to speed on activity in this field as well as a problems list, which is an expanded and edited version of problems discussed in sessions held at the conference. The problems list is intended to suggest directions for future work.
Author: I.M. James
Publisher: Springer Science & Business Media
ISBN: 1461382831
Category : Mathematics
Languages : en
Pages : 253
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Book Description
Students of topology rightly complain that much of the basic material in the subject cannot easily be found in the literature, at least not in a convenient form. In this book I have tried to take a fresh look at some of this basic material and to organize it in a coherent fashion. The text is as self-contained as I could reasonably make it and should be quite accessible to anyone who has an elementary knowledge of point-set topology and group theory. This book is based on a course of 16 graduate lectures given at Oxford and elsewhere from time to time. In a course of that length one cannot discuss too many topics without being unduly superficial. However, this was never intended as a treatise on the subject but rather as a short introductory course which will, I hope, prove useful to specialists and non-specialists alike. The introduction contains a description of the contents. No algebraic or differen tial topology is involved, although I have borne in mind the needs of students of those branches of the subject. Exercises for the reader are scattered throughout the text, while suggestions for further reading are contained in the lists of references at the end of each chapter. In most cases these lists include the main sources I have drawn on, but this is not the type of book where it is practicable to give a reference for everything.
Author: F.H. Croom
Publisher: Springer Science & Business Media
ISBN: 1468494759
Category : Mathematics
Languages : en
Pages : 187
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Book Description
This text is intended as a one semester introduction to algebraic topology at the undergraduate and beginning graduate levels. Basically, it covers simplicial homology theory, the fundamental group, covering spaces, the higher homotopy groups and introductory singular homology theory. The text follows a broad historical outline and uses the proofs of the discoverers of the important theorems when this is consistent with the elementary level of the course. This method of presentation is intended to reduce the abstract nature of algebraic topology to a level that is palatable for the beginning student and to provide motivation and cohesion that are often lacking in abstact treatments. The text emphasizes the geometric approach to algebraic topology and attempts to show the importance of topological concepts by applying them to problems of geometry and analysis. The prerequisites for this course are calculus at the sophomore level, a one semester introduction to the theory of groups, a one semester introduc tion to point-set topology and some familiarity with vector spaces. Outlines of the prerequisite material can be found in the appendices at the end of the text. It is suggested that the reader not spend time initially working on the appendices, but rather that he read from the beginning of the text, referring to the appendices as his memory needs refreshing. The text is designed for use by college juniors of normal intelligence and does not require "mathematical maturity" beyond the junior level.
Author: J. Peter May
Publisher: American Mathematical Soc.
ISBN: 0821803190
Category : Mathematics
Languages : en
Pages : 384
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Book Description
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.
