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Contour integrals as $Ad$-invariant functions on the fundamental group

Marcin Bobienski
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Abstract

We introduce a general approach to contour integrals. It covers usual Abelian integrals, the higher order Melnikov integrals and the generalized Abelian integrals. We prove that the generating function always satisfies a linear differential equation of finite order. We also present a relationship between the generalized Abelian integral and certain representation of the fundamental group of complex curve.

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Marcin Bobienski. 2005-07-11. Contour integrals as $Ad$-invariant functions on the fundamental group. https://arxiv.org/abs/math/0507213

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