Introduction To Combinatorial Torsions: Notes taken by Felix Schlenk (Lectures in Mathematics. ETH Zürich) - Softcover

Turaev, Vladimir

Softcover

ISBN 10: 3764364033 ISBN 13: 9783764364038

Verlag: Birkhäuser Verlag, 2001

Inhaltsangabe

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.

Über diesen Titel

Über die Autorin bzw. den Autor

Dr. Christian Kassel is the director of CNRS (Centre National de la Recherche Scientifique in France), was the director of l'Institut de Recherche Mathematique Avancee from 2000 to 2004, and is an editor for the Journal of Pure and Applied Algebra. Kassel has numerous publications, including the book Quantum Groups in the Springer Gradate Texts in Mathematics series. Dr. Vladimir Turaev was also a professor at the CNRS and is currently at Indiana University in the Department of Mathematics.

Details zur Ausgabe

• Verlag: Birkhäuser Verlag
• Erscheinungsdatum: 2001
• Sprache: Englisch
• ISBN 10: 3764364033
• ISBN 13: 9783764364038
• Einband: Taschenbuch
• Anzahl der Seiten: 132
• Kontakt zum Hersteller: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Deutschland