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

Yoshiaki Goto

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

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arxiv 2206.03177 v2 pith:7PDJXXZ3 submitted 2022-06-07 math.AG math.CA

Yoshiaki Goto This is my paper

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keywords integralintersectionriemann-wirtingerassociatedcohomologygroupshomologynumbers

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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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A double copy from twisted (co)homology at genus g
hep-th 2025-09 conditional novelty 7.0 of 10

A double-copy (KLT-type) formula for genus-g hypergeometric integrals is derived from twisted homology intersection numbers and verified numerically at genus two.

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