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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The cohomology representation of an action of $ C\sb p$ on a surface


Author: Peter Symonds
Journal: Trans. Amer. Math. Soc. 306 (1988), 389-400
MSC: Primary 57S17; Secondary 20C10, 57M12
MathSciNet review: 927696
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0927696-9
PII: S 0002-9947(1988)0927696-9
Article copyright: © Copyright 1988 American Mathematical Society