The analytic torsion of a disc


Autoria(s): de Melo, T.; Hartmann, L.; Spreafico, Mauro Flávio
Contribuinte(s)

UNIVERSIDADE DE SÃO PAULO

Data(s)

07/11/2013

07/11/2013

2012

Resumo

In this article, we study the Reidemeister torsion and the analytic torsion of the m dimensional disc, with the Ray and Singer homology basis (Adv Math 7:145-210, 1971). We prove that the Reidemeister torsion coincides with a power of the volume of the disc. We study the additional terms arising in the analytic torsion due to the boundary, using generalizations of the Cheeger-Muller theorem. We use a formula proved by Bruning and Ma (GAFA 16:767-873, 2006) that predicts a new anomaly boundary term beside the known term proportional to the Euler characteristic of the boundary (Luck, J Diff Geom 37:263-322, 1993). Some of our results extend to the case of the cone over a sphere, in particular we evaluate directly the analytic torsion for a cone over the circle and over the two sphere. We compare the results obtained in the low dimensional cases. We also consider a different formula for the boundary term given by Dai and Fang (Asian J Math 4:695-714, 2000), and we compare the results. The results of these work were announced in the study of Hartmann et al. (BUMI 2:529-533, 2009).

FAPESP [2010/16660-1, 2008/57607-6]

FAPESP

Identificador

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, DORDRECHT, v. 42, n. 1, pp. 29-59, JUN, 2012

0232-704X

http://www.producao.usp.br/handle/BDPI/43150

10.1007/s10455-011-9300-2

http://dx.doi.org/10.1007/s10455-011-9300-2

Idioma(s)

eng

Publicador

SPRINGER

DORDRECHT

Relação

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY

Direitos

restrictedAccess

Copyright SPRINGER

Palavras-Chave #ANALYTIC TORSION #REIDEMEISTER TORSION #FUNCTIONAL DETERMINANT #REIDEMEISTER TORSION #RIEMANNIAN MANIFOLDS #SPECTRAL GEOMETRY #R-TORSION #SPACES #LAPLACIAN #SPHERES #CONE #TOPOLOGIA ALGÉBRICA #MATHEMATICS
Tipo

article

original article

publishedVersion