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Topological theory for Selberg type integral associated with rigid Fuchsian systems

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Abstract

Using the analytic realization of middle convolution due to Dettweiler and Reiter, we show that any rigid Fuchsian system can be obtained as a subsystem of some generating system which has an integral representation of solutions of Selberg type. Twisted homology groups and twisted cohomology groups associated with such integrals are studied. In particular, contiguity relations and twisted cycles which realize local exponents are obtained.

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Authors and Affiliations

  1. Department of Mathematics, Kumamoto University, Kumamoto, 860-8555, Japan

    Yoshishige Haraoka & Sho Hamaguchi

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  1. Yoshishige Haraoka
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  2. Sho Hamaguchi
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Correspondence to Yoshishige Haraoka.

Additional information

Supported by the JSPS Grants-in-Aid for scientific research B, Nos. 17340049 and 21340038.

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Haraoka, Y., Hamaguchi, S. Topological theory for Selberg type integral associated with rigid Fuchsian systems. Math. Ann. 353, 1239–1271 (2012). https://doi.org/10.1007/s00208-011-0717-5

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  • DOI: https://doi.org/10.1007/s00208-011-0717-5

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