A Riemannian Invariant, Euler Structures and Some Topological Applications

Dan Burghelea, Stefan Haller

Veröffentlichungen: Beitrag in BuchBeitrag in Konferenzband

Abstract

First we discuss a numerical invariant associated with a Riemannian metric, a vector field with isolated zeros, and a closed one form which is defined by a geometrically regularized integral. This invariant, extends the Chern-Simons class from a pair of two Riemannian metrics to a pair of a Riemannian metric and a smooth triangulation. Next we discuss a generalization of Turaev's Euler structures to manifolds with non-vanishing Euler characteristics and introduce the Poincare dual concept of co-Euler structures. The duality is provided by a geometrically regularized integral and involves the invariant mentioned above. Euler structures have been introduced because they permit to remove the ambiguities in the definition of the Reidemeister torsion. Similarly, co-Euler structures can be used to eliminate the metric dependence of the Ray-Singer torsion. The Bismut-Zhang, Cheeger, Müller theorem can then be reformulated as a statement comparing two genuine topological invariants.
OriginalspracheEnglisch
TitelProceedings of the conference "C*-Algebras and Elliptic Theory'' held at Bedlewo, Poland 2004
Herausgeber (Verlag)Springer
Seiten37-60
Seitenumfang24
DOIs
PublikationsstatusVeröffentlicht - 2006
VeranstaltungC*-algebras and Elliptic Theory - Banach Center, Bedlewo, Polen
Dauer: 23 Jan. 200628 Jan. 2006
http://higeom.math.msu.su/bedlewo2006/

Publikationsreihe

ReiheTrends in Mathematics

Konferenz

KonferenzC*-algebras and Elliptic Theory
Land/GebietPolen
OrtBedlewo
Zeitraum23/01/0628/01/06
Internetadresse

ÖFOS 2012

  • 1010 Mathematik

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