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Synopsis
This book is an introduction to combinatorial torsions of cellular spaces and manifolds with special emphasis on torsions of 3-dimensional manifolds. The first two chapters cover algebraic foundations of the theory of torsions and various topological constructions of torsions due to K. Reidemeister, J.H.C. Whitehead, J. Milnor and the author. We also discuss connections between the torsions and the Alexander polynomials of links and 3-manifolds. The third (and last) chapter of the book deals with so-called refined torsions and the related additional structures on manifolds, specifically homological orientations and Euler structures. As an application, we give a construction of the multivariable Conway polynomial of links in homology 3-spheres. At the end of the book, we briefly describe the recent results of G. Meng, C.H. Taubes and the author on the connections between the refined torsions and the Seiberg-Witten invariant of 3-manifolds. The exposition is aimed at students, professional mathematicians and physicists interested in combinatorial aspects of topology and/or in low dimensional topology. The necessary background for the reader includes the elementary basics of topology and homological algebra.
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"[The book] contains much of the needed background material in topology and algebra...Concering the considerable material it covers, [the book] is very well-written and readable."
--Zentralblatt Math
Synopsis
This text is an introduction to combinatorial torsions of cellular spaces and manifolds with special emphasis on torsions of 3-dimensional manifolds. The necessary background for the reader includes the elementary basics of topology and homological algebra.
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Introduction to Combinatorial Torsions
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Introduction to Combinatorial Torsions
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Introduction to combinatorial torsions.
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Introduction To Combinatorial Torsions: Notes taken by Felix Schlenk (Lectures in Mathematics. ETH Zürich).
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Basel. Birkhäuser Verlag., 2001
ISBN 10: 3764364033
ISBN 13: 9783764364038
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kartoniert. Condition: Sehr gut. Zust: Gutes Exemplar. 123 Seiten, mit Abbildungen, Englisch 264g. Seller Inventory # 494383
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Introduction to Combinatorial Torsions
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Springer, Basel, Birkhäuser Basel, Birkhäuser Jan 2001, 2001
ISBN 10: 3764364033
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book is an extended version of the notes of my lecture course given at ETH in spring 1999. The course was intended as an introduction to combinatorial torsions and their relations to the famous Seiberg-Witten invariants. Torsions were introduced originally in the 3-dimensional setting by K. Rei demeister (1935) who used them to give a homeomorphism classification of 3-dimensional lens spaces. The Reidemeister torsions are defined using simple linear algebra and standard notions of combinatorial topology: triangulations (or, more generally, CW-decompositions), coverings, cellular chain complexes, etc. The Reidemeister torsions were generalized to arbitrary dimensions by W. Franz (1935) and later studied by many authors. In 1962, J. Milnor observed 3 that the classical Alexander polynomial of a link in the 3-sphere 8 can be interpreted as a torsion of the link exterior. Milnor's arguments work for an arbitrary compact 3-manifold M whose boundary is non-void and consists of tori: The Alexander polynomial of M and the Milnor torsion of M essentially coincide. 124 pp. Englisch. Seller Inventory # 9783764364038
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Introduction to Combinatorial Torsions
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book is an extended version of the notes of my lecture course given at ETH in spring 1999. The course was intended as an introduction to combinatorial torsions and their relations to the famous Seiberg-Witten invariants. Torsions were introduced originally in the 3-dimensional setting by K. Rei demeister (1935) who used them to give a homeomorphism classification of 3-dimensional lens spaces. The Reidemeister torsions are defined using simple linear algebra and standard notions of combinatorial topology: triangulations (or, more generally, CW-decompositions), coverings, cellular chain complexes, etc. The Reidemeister torsions were generalized to arbitrary dimensions by W. Franz (1935) and later studied by many authors. In 1962, J. Milnor observed 3 that the classical Alexander polynomial of a link in the 3-sphere 8 can be interpreted as a torsion of the link exterior. Milnor's arguments work for an arbitrary compact 3-manifold M whose boundary is non-void and consists of tori: The Alexander polynomial of M and the Milnor torsion of M essentially coincide. Seller Inventory # 9783764364038
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Introduction to Combinatorial Torsions
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Introduction to Combinatorial Torsions
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Introduction to Combinatorial Torsions
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Introduction to Combinatorial Torsions
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Birkhäuser Basel, 2001
ISBN 10: 3764364033
ISBN 13: 9783764364038
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Kartoniert / Broschiert. Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. I Algebraic Theory of Torsions.- 1 Torsion of chain complexes.- 2 Computation of the torsion.- 3 Generalizations and functoriality of the torsion.- 4 Homological computation of the torsion.- II Topological Theory of Torsions.- 5 Basics of algebraic topology. Seller Inventory # 5279392
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