Analytic Torsion and R-Torsion for Manifolds with Boundary

Xianzhe Dai; Hao Fang

doi:10.4310/AJM.2000.v4.n3.a10

Back

Analytic Torsion and R-Torsion for Manifolds with Boundary

Journal article

Open access

Peer reviewed

Analytic Torsion and R-Torsion for Manifolds with Boundary

Xianzhe Dai and Hao Fang

The Asian journal of mathematics : AJM., Vol.4(3), pp.695-714

01/12/1999

DOI: 10.4310/AJM.2000.v4.n3.a10

Files and links (1)

url

https://doi.org/10.4310/AJM.2000.v4.n3.a10View

Published (Version of record) Open Access

Abstract

We prove a formula relating the analytic torsion and Reidemeister torsion on manifolds with boundary in the general case when the metric is not necessarily a product near the boundary. The product case has been established by W. Lu\"ck and S. M. Vishik. We find that the extra term that comes in here in the nonproduct case is the transgression of the Euler class in the even dimensional case and a slightly more mysterious term involving the second fundamental form of the boundary and the curvature tensor of the manifold in the odd dimensional case.

Mathematics - Differential Geometry

Details

Title: Subtitle: Analytic Torsion and R-Torsion for Manifolds with Boundary
Creators: Xianzhe Dai
Hao Fang
Resource Type: Journal article
Publication Details: The Asian journal of mathematics : AJM., Vol.4(3), pp.695-714
DOI: 10.4310/AJM.2000.v4.n3.a10
ISSN: 1093-6106
eISSN: 1945-0036
Language: English
Date published: 01/12/1999
Academic Unit: Mathematics
Record Identifier: 9984242359002771

Metrics

21 Record Views