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- W2045067311 abstract "Holomorphic forms are integrated iteratedly along paths in a compact Riemann surface $M$ of genus $g$, thus inducing a homomorphism from the fundamental group $Gamma = {pi _1}(M,{P_0})$ to a proper multiplicative subgroup $G$ of the group of units in $widehat {T({Omega ^{1 ast }})}$, where ${Omega ^1}$ denotes the space of holomorphic forms on $T$ is the complex dual of ${Omega ^1}$, $T$ means the associated tensor algebra and 11$hat { }$â means completion with respect to the natural grading. The associated homomorphisms from $Gamma /{Gamma ^{(n + 1)}}$ to $G/{G^{(n + 1)}}$ reduces to the classical case ${H_1}(M) to {Omega ^{1 ast }}$ when $n = 1$. We show that the images of $Gamma /{Gamma ^{(n + 1)}}$ are always cocompact in $G/{G^{(n + 1)}}$ and are discrete for all $n geqslant 2$ if and only if the Jacobian variety $J(M)$ of $M$ is isogenous to ${E^g}$ for some elliptic curve $E$ with complex multiplication." @default.
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- W2045067311 date "1981-02-01" @default.
- W2045067311 modified "2023-09-27" @default.
- W2045067311 title "Periods of iterated integrals of holomorphic forms on a compact Riemann surface" @default.
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- W2045067311 doi "https://doi.org/10.1090/s0002-9947-1981-0603764-x" @default.
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