Introduction to Combinatorial Torsions is popular PDF and ePub book, written by Vladimir Turaev in 2012-12-06, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Introduction to Combinatorial Torsions can be Read Online from any device for your convenience.
Introduction to Combinatorial Torsions Book PDF Summary
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.
Detail Book of Introduction to Combinatorial Torsions PDF
- Author : Vladimir Turaev
- Release : 06 December 2012
- Publisher : Birkhäuser
- ISBN : 9783034883214
- Genre : Mathematics
- Total Page : 128 pages
- Language : English
- PDF File Size : 11,6 Mb
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