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A Cheeger–Müller theorem for Cappell–Miller torsions on manifolds with boundary

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Abstract

In this paper, we extend the Cappell–Miller analytic torsion to manifolds with boundary under the absolute and relative boundary conditions and using the techniques of Brüning-Ma and Su-Zhang, we get the anomaly formula of it for odd dimensional manifolds. Then by the methods of Brüning-Ma, Cappell–Miller and Su-Zhang, we get the Cheeger–Müller theorem for the Cappell–Miller analytic torsion on odd dimensional manifolds with boundary up to a sign. As a consequence of the main theorem, we get the gluing formula for the Cappell–Miller analytic torsion which generalizes a theorem of Huang.

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Authors and Affiliations

  1. Chern Institute of Mathematics and LPMC, Nankai University, Tianjin, 300071, People’s Republic of China

    Guangxiang Su

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  1. Guangxiang Su
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Correspondence to Guangxiang Su.

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Supported by NSFC11571183.

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Su, G. A Cheeger–Müller theorem for Cappell–Miller torsions on manifolds with boundary. manuscripta math. 149, 369–388 (2016). https://doi.org/10.1007/s00229-015-0787-x

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  • DOI: https://doi.org/10.1007/s00229-015-0787-x

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