Intersection numbers of twisted homology and cohomology groups associated to the Riemann-Wirtinger integral

2022/06/07 by Yoshiaki Goto, Goto, Yoshiaki · 1 citation
Mathematics · #14K25 #33C99 #55N25 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2206.03177

openalex publication_date 2022/06/07 · openalex created_date 2022/06/13 · openalex updated_date 2026/07/28

Abstract

The Riemann-Wirtinger integral is an analogue of the hypergeometric integral, which is defined as an integral on a one-dimensional complex torus. We study the intersection forms on the twisted homology and cohomology groups associated with the Riemann-Wirtinger integral. We derive explicit formulas of some intersection numbers, and apply them to study the monodromy representation, connection problems, and contiguity relations.

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• Notes on twisted homology and cohomology groups for the Wirtinger integral

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