This project lies in the interface of three manifolds and the representations of finite groups. Let G be a finite group that acts on a compact orientable surface S of genus g at least two. The question is whether the action can be extended to a compact orientable three manifold V with boundary S. The only known answers are the Hurwitz actions of PSL(2,q) for q a prime and some classes of finite groups of prime power order. Along with the recent development that connects the free actions of a finite group G with the Schur Multiplier of G, we would like to extend this work to answer the extendibility for all possible actions of a certain class of groups.
Indian Institute of Science
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