The cohomology representation of an action of 𝐶_{𝑝} on a surface

Symonds, Peter

doi:10.1090/S0002-9947-1988-0927696-9

The cohomology representation of an action of $C_ p$ on a surface
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by Peter Symonds

Trans. Amer. Math. Soc. 306 (1988), 389-400

DOI: https://doi.org/10.1090/S0002-9947-1988-0927696-9

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Abstract:

When a finite group $G$ acts on a surface $S$, then ${H^1}(S; {\mathbf {Z}})$ posseses naturally the structure of a ${\mathbf {Z}}G$-module with invariant symplectic inner product. In the case of a cyclic group of odd prime order we describe explicitly this symplectic inner product space in terms of the fixed-point data of the action.

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