Introduction To Combinatorial Torsions - Couverture souple

Turaev, Vladimir

 
9783764364038: Introduction To Combinatorial Torsions
Couverture souple
ISBN 10 : 3764364033 ISBN 13 : 9783764364038
Editeur : Birkhäuser Basel, 2001

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

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.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Birkhäuser Basel
Date d'édition
2001
Langue
anglais
ISBN 10 
3764364033
ISBN 13 
9783764364038
Reliure
Broché
Nombre de pages
132
Coordonnées du fabricant
non disponible
Personne responsable
non disponible

Autres éditions populaires du même titre

9783034883221: Introduction to Combinatorial Torsions

Edition présentée

ISBN 10 :  3034883226 ISBN 13 :  9783034883221
Editeur : Birkhäuser, 2011
Couverture souple