Cw Complexes Homology Theory
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The Topology Of Cw Complexes
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Author : A.T. Lundell
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Topology Of Cw Complexes written by A.T. Lundell 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.
Most texts on algebraic topology emphasize homological algebra, with topological considerations limited to a few propositions about the geometry of simplicial complexes. There is much to be gained however, by using the more sophisticated concept of cell (CW) complex. Even for simple computations, this concept ordinarily allows us to bypass much tedious algebra and often gives geometric insight into the homology and homotopy theory of a space. For example, the easiest way to calculate and interpret the homology of Cpn, complex projective n-space, is by means of a cellular decomposition with only n+ 1 cells. Also, by a suitable construction we can "realize" the sin gular complex of a space as a CW complex and perhaps thus give a more geometric basis for some arguments involving singular homology theory for general spaces and a more concrete basis for singular ho motopy type. As a fInal example, if we start with the category of sim plicial complexes and maps, common topological constructions such as the formation of product spaces, identifIcation spaces, and adjunction spaces lead us often into the category of CW complexes. These topics, among others, are usually not treated thoroughly in a standard text, and the interested student must fInd them scattered through the literature. This book is a study of CW complexes. It is intended to supplement and be used concurrently with a standard text on algebraic topology.
Cw Complexes Homology Theory
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Author : Renzo A. Piccinini
language : en
Publisher: Kingston, Ont. : Queen's University
Release Date : 1973
Cw Complexes Homology Theory written by Renzo A. Piccinini and has been published by Kingston, Ont. : Queen's University this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with CW complexes categories.
Cellular Structures In Topology
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Author : Rudolf Fritsch
language : en
Publisher: Cambridge University Press
Release Date : 1990-09-27
Cellular Structures In Topology written by Rudolf Fritsch 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 1990-09-27 with Mathematics categories.
This book describes the construction and the properties of CW-complexes. These spaces are important because firstly they are the correct framework for homotopy theory, and secondly most spaces that arise in pure mathematics are of this type. The authors discuss the foundations and also developments, for example, the theory of finite CW-complexes, CW-complexes in relation to the theory of fibrations, and Milnor's work on spaces of the type of CW-complexes. They establish very clearly the relationship between CW-complexes and the theory of simplicial complexes, which is developed in great detail. Exercises are provided throughout the book; some are straightforward, others extend the text in a non-trivial way. For the latter; further reference is given for their solution. Each chapter ends with a section sketching the historical development. An appendix gives basic results from topology, homology and homotopy theory. These features will aid graduate students, who can use the work as a course text. As a contemporary reference work it will be essential reading for the more specialized workers in algebraic topology and homotopy theory.
Homology Theory
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Author : James W. Vick
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Homology Theory written by James W. Vick 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 introduction to some basic ideas in algebraic topology is devoted to the foundations and applications of homology theory. After the essentials of singular homology and some important applications are given, successive topics covered include attaching spaces, finite CW complexes, cohomology products, manifolds, Poincare duality, and fixed point theory. This second edition includes a chapter on covering spaces and many new exercises.
Cellular Structures In Topology
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Author : Rudolf Fritsch
language : en
Publisher: Cambridge University Press
Release Date : 1990-09-27
Cellular Structures In Topology written by Rudolf Fritsch 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 1990-09-27 with Mathematics categories.
This book describes the construction and the properties of CW-complexes. These spaces are important because firstly they are the correct framework for homotopy theory, and secondly most spaces that arise in pure mathematics are of this type. The authors discuss the foundations and also developments, for example, the theory of finite CW-complexes, CW-complexes in relation to the theory of fibrations, and Milnor's work on spaces of the type of CW-complexes. They establish very clearly the relationship between CW-complexes and the theory of simplicial complexes, which is developed in great detail. Exercises are provided throughout the book; some are straightforward, others extend the text in a non-trivial way. For the latter; further reference is given for their solution. Each chapter ends with a section sketching the historical development. An appendix gives basic results from topology, homology and homotopy theory. These features will aid graduate students, who can use the work as a course text. As a contemporary reference work it will be essential reading for the more specialized workers in algebraic topology and homotopy theory.
Homotopy Type And Homology
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Author : Hans J. Baues
language : en
Publisher: Oxford University Press
Release Date : 1996
Homotopy Type And Homology written by Hans J. Baues and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
This monograph represents an attempt to classify homotopy types of simply connected CW-complexes. It provides methods and examples of explicit homotopy classifications, and includes applications to the classification of manifolds.
Singular Homology Theory
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Author : W.S. Massey
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Singular Homology Theory written by W.S. Massey 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 textbook on homology and cohomology theory is geared towards the beginning graduate student. Singular homology theory is developed systematically, avoiding all unnecessary definitions, terminology, and technical machinery. Wherever possible, the geometric motivation behind various algebraic concepts is emphasized. The only formal prerequisites are knowledge of the basic facts of abelian groups and point set topology. Singular Homology Theory is a continuation of t he author's earlier book, Algebraic Topology: An Introduction, which presents such important supplementary material as the theory of the fundamental group and a thorough discussion of 2-dimensional manifolds. However, this earlier book is not a prerequisite for understanding Singular Homology Theory.
Combinatorial Foundation Of Homology And Homotopy
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Author : Hans-Joachim Baues
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Combinatorial Foundation Of Homology And Homotopy written by Hans-Joachim Baues 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 2013-03-09 with Mathematics categories.
A new combinatorial foundation of the two concepts, based on a consideration of deep and classical results of homotopy theory, and an axiomatic characterization of the assumptions under which results in this field hold. Includes numerous explicit examples and applications in various fields of topology and algebra.
Generalized Cohomology
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Author : Akira Kōno
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Generalized Cohomology written by Akira Kōno 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 Mathematics categories.
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.
Intersection Spaces Spatial Homology Truncation And String Theory
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Author : Markus Banagl
language : en
Publisher: Springer
Release Date : 2010-06-16
Intersection Spaces Spatial Homology Truncation And String Theory written by Markus Banagl and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-16 with Mathematics categories.
Intersection cohomology assigns groups which satisfy a generalized form of Poincaré duality over the rationals to a stratified singular space. This monograph introduces a method that assigns to certain classes of stratified spaces cell complexes, called intersection spaces, whose ordinary rational homology satisfies generalized Poincaré duality. The cornerstone of the method is a process of spatial homology truncation, whose functoriality properties are analyzed in detail. The material on truncation is autonomous and may be of independent interest tohomotopy theorists. The cohomology of intersection spaces is not isomorphic to intersection cohomology and possesses algebraic features such as perversity-internal cup-products and cohomology operations that are not generally available for intersection cohomology. A mirror-symmetric interpretation, as well as applications to string theory concerning massless D-branes arising in type IIB theory during a Calabi-Yau conifold transition, are discussed.