Abstract:For G and H 1 , . . . , H n finite groups, does there exist a 3-manifold group with G as a quotient but no H i as a quotient? We answer all such questions in terms of the group cohomology of finite groups. We prove non-existence with topological results generalizing the theory of semicharacteristics. To prove existence of 3-manifolds with certain finite quotients but not others, we use a probabilistic method, by first proving a formula for the distribution of the (profinite completion of) the fundamental group… Show more
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