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Greg Kuperberg, RLM 12.166: Intractability of finite quotients of 3-manifold groups
Monday, March 25, 2019, 02:00pm - 03:00pm
The number of homomorphisms from the fundamental group of a topologicalspace X to a target finite group G is a useful invariant in geometrictopology, in particular when X = M is a closed 3-manifold ora knot complement. However, we can show that this invariantis computationally intractable in these cases when G is a fixedfinite simple group and M is sufficiently complicated. In effect,M is a programmable object, the existence of a non-trivial homomorphismis NP-complete, and counting homomorphisms is harder still. The machine behind the programmability of M is a mutual generalizationand refinement of the Conway-Parker-Dunfield-Thurston theoremon the transitivity of the mapping class group action on theset of homomorphisms from a surface group to G.
Location: RLM 12.166

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