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Introduction to Combinatorial Torsions

Af: Vladimir Turaev Engelsk Paperback

Introduction to Combinatorial Torsions

Af: Vladimir Turaev Engelsk Paperback
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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.
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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.
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Se mere i:
Produktdetaljer
Sprog: Engelsk
Sider: 124
ISBN-13: 9783764364038
Indbinding: Paperback
Udgave:
ISBN-10: 3764364033
Kategori: Differential- og Riemannsk geometri
Udg. Dato: 1 jan 2001
Længde: 0mm
Bredde: 170mm
Højde: 244mm
Forlag: Birkhauser Verlag AG
Oplagsdato: 1 jan 2001
Forfatter(e): Vladimir Turaev
Forfatter(e) Vladimir Turaev

Kategori Differential- og Riemannsk geometri

ISBN-13 9783764364038

Sprog Engelsk

Indbinding Paperback

Sider 124

Udgave

Længde 0mm

Bredde 170mm

Højde 244mm

Udg. Dato 1 jan 2001

Oplagsdato 1 jan 2001

Forlag Birkhauser Verlag AG