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Comparison between two analytic torsions on orbifolds

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Abstract

In this paper, we establish an equality between the analytic torsion introduced by Dar (Math Z 194(2): 193–216, 1987) and the orbifold analytic torsion defined by Ma (Trans Am Math Soc 357(6): 2205–2233, 2005) on an even dimensional manifold with isolated conical singularities which in addition has an orbifold structure. We assume the orbifold flat vector bundle is an honest vector bundle, although the metric on the flat bundle may not be flat.

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Acknowledgments

The first author is supported by the Simons Foundation and NSFC. The work was carried out while the second author was visiting the University of California, Santa Barbara (UCSB). He would like to thank the hospitality of the Department of Mathematics in UCSB and the financial support from the program of China Scholarships Council. The authors thank the referee for many constructive suggestions.

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Authors and Affiliations

  1. Department of Mathematics, ECNU, Shanghai, People’s Republic of China

    Xianzhe Dai

  2. UCSB, Santa Barbara, CA, 93106, USA

    Xianzhe Dai

  3. School of Mathematical Sciences, University of Science and Technology of China, 96 Jinzhai Road, Hefei, 230026, Anhui, People’s Republic of China

    Jianqing Yu

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  1. Xianzhe Dai
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  2. Jianqing Yu
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Correspondence to Xianzhe Dai.

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Dai, X., Yu, J. Comparison between two analytic torsions on orbifolds. Math. Z. 285, 1269–1282 (2017). https://doi.org/10.1007/s00209-016-1747-1

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  • DOI: https://doi.org/10.1007/s00209-016-1747-1

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