\(L^ 2\)-index theorems on locally symmetric spaces
type: Item
instance of: scholarly article
title: \(L^ 2\)-index theorems on locally symmetric spaces
zbMATH Open document ID: 0694.58039
DOI: 10.1007/BF01393964
author: Mark Stern
published in: Inventiones Mathematicae
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143679
review text: Let G be a real semisimple Lie group, K a maximal compact subgroup, and \(\Gamma\) a neat arithmetic subgroup. If the \({\mathbb{Q}}\)-rank of G is greater than zero, then \(\Gamma\setminus G/K\) is a noncompact, finite volume, locally symmetric space. The main aim of this paper is to extend the Atiyah-Singer index theorem to an \(L^ 2\)-index theorem in this situation.
Mathematics Subject Classification ID: 58J20
Mathematics Subject Classification ID: 53C35
zbMATH DE Number: 4137069
zbMATH Keywords: semisimple Lie group
zbMATH Keywords: maximal compact subgroup
zbMATH Keywords: Atiyah-Singer index theorem
MaRDI profile type: Publication
cites work: Q4099744
cites work: On the heat equation and the index theorem
cites work: Clifford modules
cites work: Eta invariants, signature defects of cusps, and values of L-functions
cites work: Spectral asymmetry and Riemannian Geometry. I
cites work: Compactification of arithmetic quotients of bounded symmetric domains
cites work: \(L^ 2\)-index and the Selberg trace formula
cites work: Q3278470
cites work: Stable real cohomology of arithmetic groups
cites work: Q3328657
cites work: \(L^ 2\)-cohomology of locally symmetric manifolds of finite volume
cites work: Q3752500
cites work: Axial anomalies and index theorems on open spaces
cites work: Functional determinants in Euclidean Yang-Mills theory
cites work: Q3969051
cites work: Essential self-adjointness of powers of generators of hyperbolic equations
cites work: Q3223360
cites work: On the cuspidal spectrum for finite volume symmetric spaces
cites work: Pure point spectrum and negative curvature for noncompact manifolds
cites work: Q4119838
cites work: Q5509277
cites work: Pseudodifferential operators on supermanifolds and the Atiyah-Singer index theorem
cites work: Positive scalar curvature and the Dirac operator on complete Riemannian manifolds
cites work: Hilbert modular surfaces
cites work: Lie algebra cohomology and the generalized Borel-Weil theorem
cites work: A family of Fourier integral operators and the fundamental solution for a Schrödinger equation
cites work: On the cohomology groups attached to certain vector valued differential forms on the product of the upper half planes
cites work: Closed geodesics and the \(\eta\)-invariant
cites work: 𝐿²-index of elliptic operators on locally symmetric spaces of finite volume
cites work: The signature with local coefficients of locally symmetric spaces
cites work: Signature defects of cusps of Hilbert modular varieties and values of L- series at \(s=1\)
cites work: Curvature and the eigenforms of the Laplace operator
cites work: L 2 -cohomology of arithmetic varieties
cites work: L//2 cohomology of warped products and arithmetic groups
cites work: Q3762441
OpenAlex ID: W1993993275
description: scientific article; zbMATH DE number 4137069