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Author: S. Buoncristiano
Publisher: Cambridge University Press
ISBN: 0521209404
Category : Mathematics
Languages : en
Pages : 157
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Book Description
The purpose of these notes is to give a geometrical treatment of generalized homology and cohomology theories. The central idea is that of a 'mock bundle', which is the geometric cocycle of a general cobordism theory, and the main new result is that any homology theory is a generalized bordism theory. The book will interest mathematicians working in both piecewise linear and algebraic topology especially homology theory as it reaches the frontiers of current research in the topic. The book is also suitable for use as a graduate course in homology theory.
Author: S. Buoncristiano
Publisher: Cambridge University Press
ISBN: 0521209404
Category : Mathematics
Languages : en
Pages : 157
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Book Description
The purpose of these notes is to give a geometrical treatment of generalized homology and cohomology theories. The central idea is that of a 'mock bundle', which is the geometric cocycle of a general cobordism theory, and the main new result is that any homology theory is a generalized bordism theory. The book will interest mathematicians working in both piecewise linear and algebraic topology especially homology theory as it reaches the frontiers of current research in the topic. The book is also suitable for use as a graduate course in homology theory.
Author: Colin Patrick Rourke
Publisher:
ISBN:
Category : Homology theory
Languages : en
Pages : 84
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Book Description
Author: James W. Vick
Publisher: Springer Science & Business Media
ISBN: 1461208815
Category : Mathematics
Languages : en
Pages : 258
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Book Description
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.
Author: Mahima Ranjan Adhikari
Publisher: Springer Nature
ISBN: 9811665508
Category : Mathematics
Languages : en
Pages : 488
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Book Description
This third of the three-volume book is targeted as a basic course in algebraic topology and topology for fiber bundles for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, and algebra. Topics covered in this volume include homotopy theory, homology and cohomology theories, homotopy theory of fiber bundles, Euler characteristic, and the Betti number. It also includes certain classic problems such as the Jordan curve theorem along with the discussions on higher homotopy groups and establishes links between homotopy and homology theories, axiomatic approach to homology and cohomology as inaugurated by Eilenberg and Steenrod. It includes more material than is comfortably covered by beginner students in a one-semester course. Students of advanced courses will also find the book useful. This book will promote the scope, power and active learning of the subject, all the while covering a wide range of theory and applications in a balanced unified way.
Author: Viktor Vasilʹevich Prasolov
Publisher: American Mathematical Soc.
ISBN: 0821838121
Category : Mathematics
Languages : en
Pages : 432
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Book Description
The book is a continuation of the previous book by the author (Elements of Combinatorial and Differential Topology, Graduate Studies in Mathematics, Volume 74, American Mathematical Society, 2006). It starts with the definition of simplicial homology and cohomology, with many examples and applications. Then the Kolmogorov-Alexander multiplication in cohomology is introduced. A significant part of the book is devoted to applications of simplicial homology and cohomology to obstruction theory, in particular, to characteristic classes of vector bundles. The later chapters are concerned with singular homology and cohomology, and Cech and de Rham cohomology. The book ends with various applications of homology to the topology of manifolds, some of which might be of interest to experts in the area. The book contains many problems; almost all of them are provided with hints or complete solutions.
Author: William Pardon
Publisher: American Mathematical Soc.
ISBN: 0821821962
Category : Cuba
Languages : en
Pages : 187
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Book Description
In the monograph under consideration here the author develops the geometry of the situation, for any [lowercase Greek]Pi. The main tool is the notion of "a local surgery on a conglomerate Moore space'', which is a sequence of surgeries on a normal map [script]f such that each of the maps in the trace ([italic]g;[script]f,[script]fʹ):([italic]N;M,Mʹ) [right arrow]→[italic]X is a rational homotopy equivalence. It is possible to perform local surgery below the middle dimension to make an n-dimensional rational homotopy equivalence [([italic]n−2)/2]-connected, and to prove a local [lowercase Greek]Pi −[lowercase Greek]Pi theorem, so that the global local surgery obstruction is the Witt class of the linking form on the remaining kernel torsion modules. This brief summary belies the technical difficulties which have to be overcome in the process, particularly the geometric intersection theory of local surgery.
Author: Robert Messer
Publisher: American Mathematical Soc.
ISBN: 1470447819
Category : Mathematics
Languages : en
Pages : 254
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Book Description
Topology is a branch of mathematics packed with intriguing concepts, fascinating geometrical objects, and ingenious methods for studying them. The authors have written this textbook to make the material accessible to undergraduate students without requiring extensive prerequisites in upper-level mathematics. The approach is to cultivate the intuitive ideas of continuity, convergence, and connectedness so students can quickly delve into knot theory, the topology of surfaces and three-dimensional manifolds, fixed points and elementary homotopy theory. The fundamental concepts of point-set topology appear at the end of the book when students can see how this level of abstraction provides a sound logical basis for the geometrical ideas that have come before. This organization exposes students to the exciting world of topology now(!) rather than later. Students using this textbook should have some exposure to the geometry of objects in higher-dimensional Euclidean spaces together with an appreciation of precise mathematical definitions and proofs.
Author: P. J. Cameron
Publisher: Cambridge University Press
ISBN: 0521283787
Category : Mathematics
Languages : en
Pages : 381
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Book Description
This 1981 collection of 33 research papers follows from a conference on the interwoven themes of finite Desarguesian spaces and Steiner systems, amongst other topics.
Author: Neal Koblitz
Publisher: Cambridge University Press
ISBN: 0521280605
Category : Mathematics
Languages : en
Pages : 171
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Book Description
An introduction to recent work in the theory of numbers and its interrelation with algebraic geometry and analysis.
Author:
Publisher: CUP Archive
ISBN:
Category :
Languages : en
Pages : 196
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Book Description
