|
|||||
|
|
|
|
|
|
|
|
|
Euler structures, the
variety of representations and the Milnor–Turaev torsion
Dan Burghelea and Stefan Haller |
|
Geometry & Topology 10 (2006) 1185–1238
|
|
arXiv: math.DG/0310154 |
Abstract |
|
In this paper we extend and Poincaré dualize the concept of Euler structures, introduced by Turaev for manifolds with vanishing Euler–Poincaré characteristic, to arbitrary manifolds. We use the Poincaré dual concept, co-Euler structures, to remove all geometric ambiguities from the Ray–Singer torsion by providing a slightly modified object which is a topological invariant. We show that when the co-Euler structure is integral then the modified Ray–Singer torsion when regarded as a function on the variety of generically acyclic complex representations of the fundamental group of the manifold is the absolute value of a rational function which we call in this paper the Milnor–Turaev torsion. |
Keywords
Euler structure, co-Euler structure, combinatorial torsion,
analytic torsion, theorem of Bismut–Zhang, Chern–Simons
theory, geometric regularization, mapping torus, rational
function
|
Mathematical Subject Classification 2000
Primary: 57R20
Secondary: 58J52
|
References |
Forward citations |
Publication
Received: 16 December 2005
Revised: 27 March 2006
Accepted: 23 July 2006
Published: 16 September 2006
Proposed: Wolfgang Lück
Seconded: Bill Dwyer, Haynes Miller
|
Authors |
| Dan Burghelea | |
| Dept. of Mathematics The Ohio State University 231 West 18th Avenue Columbus, OH 43210 USA |
|
| Stefan Haller | |
| Department of Mathematics University of Vienna Nordbergstrasse 15 A-1090, Vienna Austria |
|
|
