The analytic torsion of a disc |
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Authors: | T de Melo L Hartmann M Spreafico |
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Institution: | 1. UNESP, Universidade Estadual Paulista, Rio Claro, Brazil 2. UFSCar, Universidade Federal de S?o Carlos, S?o Carlos, Brazil 3. ICMC, Universidade de S?o Paulo, S?o Carlos, Brazil
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Abstract: | 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–Müller theorem. We use a formula
proved by Brüning 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
(Lück, 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). |
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