The analytic torsion of a disc

Autor(es)

de Melo, T. ^[1] ; Hartmann, L. ^[2] ; Spreafico, M. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Estadual Paulista, Rio Claro - Brazil

^[2] Univ Fed Sao Carlos, UFSCar, BR-13560 Sao Carlos, SP - Brazil

^[3] Univ Sao Paulo, ICMC, Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: ANNALS OF GLOBAL ANALYSIS AND GEOMETRY; v. 42, n. 1, p. 29-59, JUN 2012.
• Citações Web of Science: 3

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). (AU)

• Processo FAPESP: 10/16660-1 - Invariantes de torção para pseudovariedades
• Beneficiário: Luiz Roberto Hartmann Junior
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 08/57607-6 - Topologia algébrica geométrica e diferencial
• Beneficiário: Daciberg Lima Gonçalves
• Modalidade de apoio: Auxílio à Pesquisa - Temático