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Title:
Lecture 1: Finite Quotients of 3-manifold groups
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Abstract:
It is well-known that for any finite group G, there exists a closed 3-manifold M with G as a quotient of the fundamental group of M. However, we can ask more detailed questions about the possible finite quotients of 3-manifold groups, e.g. for G and H1,...,Hn finite groups, does there exist a 3-manifold group with G as a quotient but no Hi as a quotient? We answer all such questions. To prove non-existence, we prove new parity properties of the fundamental groups of 3-manifolds. To prove existence of 3-manifolds with certain finite quotients but not others, we use a
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