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Parallel Transport Along Seifert Manifolds and Fractional Monodromy

Abstract

The notion of fractional monodromy was introduced by Nekhoroshev, Sadovskií and Zhilinskií as a generalization of standard (‘integer’) monodromy in the sense of Duistermaat from torus bundles to singular torus fibrations. In the present paper we prove a general result that allows one to compute fractional monodromy in various integrable Hamiltonian systems. In particular, we show that the non-triviality of fractional monodromy in 2 degrees of freedom systems with a Hamiltonian circle action is related only to the fixed points of the circle action. Our approach is based on the study of a specific notion of parallel transport along Seifert manifolds.

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Correspondence to N. Martynchuk.

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Communicated by J. Marklof

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Martynchuk, N., Efstathiou, K. Parallel Transport Along Seifert Manifolds and Fractional Monodromy. Commun. Math. Phys. 356, 427–449 (2017). https://doi.org/10.1007/s00220-017-2988-5

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  • DOI: https://doi.org/10.1007/s00220-017-2988-5