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- W3167442945 abstract "We study the algebraic conditions leading to the chain property of complexes for vertex operator algebra $n$-point functions with differential being defined through reduction formulas. The notion of the reduction cohomology of Riemann surfaces is introduced. Algebraic, geometrical, and cohomological meanings of reduction formulas is clarified. A counterpart of the Bott-Segal theorem for Riemann surfaces in terms of the reductions cohomology is proven. It is shown that the reduction cohomology is given by the cohomology of $n$-point connections over the vertex operator algebra bundle defined on a genus $g$ Riemann surface $Sigma^{(g)}$. The reduction cohomology for a vertex operator algebra with formal parameters identified with local coordinates around marked points on $Sigma^{(g)}$ is found in terms of the space of analytical continuations of solutions to Knizhnik-Zamolodchikov equations. For the reduction cohomology, the Euler-Poincare formula is derived. Examples for various genera and vertex operator cluster algebras are provided." @default.
- W3167442945 created "2021-06-22" @default.
- W3167442945 creator A5038812456 @default.
- W3167442945 date "2021-06-11" @default.
- W3167442945 modified "2023-09-27" @default.
- W3167442945 title "Reduction cohomology of Riemann surfaces" @default.
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- W3167442945 doi "https://doi.org/10.48550/arxiv.2106.06541" @default.
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