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- W4287601980 abstract "We consider the moduli space ${cal M}(G)$ of $G$-Higgs bundles over a compact Riemann surface $X$, where $G$ is a semisimple complex Lie group, and study the action of a finite group $Gamma$ on ${cal M}(G)$ induced by a holomorphic action of $Gamma$ on $X$ and $G$, and a character of $Gamma$. The fixed-point subvariety for this action is given by a union of moduli spaces of $G$-Higgs bundles equipped with a certain twisted $Gamma$-equivariant structure involving a $2$-cocycle of $Gamma$ with values in the centre of $G$. This union is paremeterized by the non-abelian first cohomology set of $Gamma$ in the adjoint group of $G$. We also describe the fixed points in the moduli space of representations of the fundamental group of $X$ in $G$, via a twisted equivariant version of the non-abelian Hodge correspondence, which involves the $Gamma$-equivariant fundamental group of $X$." @default.
- W4287601980 created "2022-07-25" @default.
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- W4287601980 date "2020-11-08" @default.
- W4287601980 modified "2023-10-17" @default.
- W4287601980 title "Finite group actions on Higgs bundle moduli spaces and twisted equivariant structures" @default.
- W4287601980 doi "https://doi.org/10.48550/arxiv.2011.04017" @default.
- W4287601980 hasPublicationYear "2020" @default.
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