Cohomology of multipoint connections on complex curves
A. Zuevsky

TL;DR
This paper develops a cohomology theory for multipoint connections on complex curves using generalized holomorphic connections, with explicit examples involving higher genus elliptic functions and functional equations.
Contribution
It introduces a novel cohomology framework for multipoint connections on complex curves based on generalized holomorphic connections.
Findings
Cohomology expressed via higher genus elliptic functions
Explicit solutions obtained through analytic continuation
Functional equations related to complex curve connections
Abstract
Assuming complex functions defined on complex curves satisfy recursion relations with respect to number of parameters, we express the corresponding cohomology theory via generalizations of holomorphic connections. In examples provided, the cohomology is explicitly found in terms of higher genus counterparts of elliptic functions as analytic continuations of solutions for functional equations.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Algebraic Geometry and Number Theory · Nonlinear Waves and Solitons
