Euler structures, the variety of representations and the Milnor-Turaev torsion

Stefan Haller, Dan Burghelea

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed


In this paper we extend, and Poincare dualize, the concept of Euler structures, introduced by Turaev for manifolds with vanishing Euler-Poincare characteristic, to arbitrary manifolds. We use the Poincare 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.
Seiten (von - bis)1185-1238
FachzeitschriftGeometry & Topology
PublikationsstatusVeröffentlicht - 2006

ÖFOS 2012

  • 1010 Mathematik