Ray–Singer Torsion and the Rumin Laplacian on Lens Spaces

Akira Kitaoka

Graduate School of Mathematical Sciences, The University of Tokyo, Japan

Abstract: We express explicitly the analytic torsion functions associated with the Rumin complex on lens spaces in terms of the Hurwitz zeta function. In particular, we find that the functions vanish at the origin and determine the analytic torsions. Moreover, we have a formula between this torsion and the Ray–Singer torsion.

Keywords: analytic torsion, Rumin complex, CR geometry, contact geometry.

MSC: 58J52, 32V20, 53D10, 43A85

Received: May 19, 2022; in final form November 14, 2022; Published online November 28, 2022

Language: English

DOI: 10.3842/SIGMA.2022.091

Bibliographic databases:

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ArXiv: 2009.03276