Finite Abelian actions on surfaces |
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Authors: | AA George Michael |
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Institution: | Department of Mathematics, Voorhees College, Denmark, SC 29042, USA |
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Abstract: | Edmonds showed that two free orientation preserving smooth actions φ1 and φ2 of a finite Abelian group G on a closed connected oriented smooth surface M are equivalent by an equivariant orientation preserving diffeomorphism iff they have the same bordism class M,φ1]=M,φ2] in the oriented bordism group Ω2(G) of the group G. In this paper, we compute the bordism class M,φ] for any such action of G on M and we determine for a given M, the bordism classes in Ω2(G) that are representable by such actions of G on M. This will enable us to obtain a formula for the number of inequivalent such actions of G on M. We also determine the “weak” equivalence classes of such actions of G on M when all the p-Sylow subgroups of G are homocyclic (i.e. of the form n(Z/pαZ)). |
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Keywords: | 57S17 57S25 |
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