Equivariant torsion of locally symmetric spaces

Anton Deitmar

Type: Article

Publication Date: 1998-02-01

Citations: 4

DOI: https://doi.org/10.2140/pjm.1998.182.205

Abstract

In this paper we express the equivariant torsion of an Hermitian locally symmetric space in terms of geometrical data from closed geodesics and their Poincaré maps.For a Hermitian locally symmetric space Y and a holomorphic isometry g we define a zeta function Z g (s) for (s) 0, whose definition involves closed geodesics and their Poincaré maps.We show that Z g extends meromorphically to the entire plane and that its leading coefficient at s = 0 equals the quotient of the equivariant torsion over the equivariant L 2torsion.

Locations

Pacific Journal of Mathematics - View - PDF

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+	Delocalized L2-Invariants	1999	John Lott
+	Arithmetic Groups and Their Generalizations	2009	Lizhen Ji
+	L2-Invariants of Regular Coverings of Compact Manifolds and CW-Complexes	2001	Wolfgang Lück
+	Analytic torsion of all vector bundles over an elliptic curve	2001	Alain Berthomieu

Works Cited by This (15)

Action	Title	Year	Authors
+ PDF Chat	Discrete series for semisimple Lie groups I: Construction of invariant eigendistributions	1965	Harish-chandra Harish-Chandra
+ PDF Chat	Cohomologie des groupes discrets	1971	Jean-Pierre Serre
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+ PDF Chat	Equivariant immersions and Quillen metrics	1995	Jean‐Michel Bismut
+ PDF Chat	Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds	1982	Jeff Cheeger M. Gromov Michael E. Taylor
+ PDF Chat	L 2-topological invariants of 3-manifolds	1995	John Lott Wolfgang L�ck
+	Delocalized $L^2$-Invariants	1996	John Lott
+	Higher Torsion Zeta Functions	1995	Anton Deitmar
+	Introduction aux groupes arithmétiques	1969	Armand Borel
+	Von Neumann spectra near zero	1991	M. Gromov Mikhail Shubin