The curious moduli spaces of unmarked Kleinian surface groups

Details The curious moduli spaces of unmarked Kleinian surface groups The curious moduli spaces of unmarked Kleinian surface groups

2009-06-30

arxiv.org/abs/0906.5601v2

Mathematics

Geometric Topology

15 pages

Scientific paper

Fixing a closed hyperbolic surface S, we define a moduli space AI(S) of unmarked hyperbolic 3-manifolds homotopy equivalent to S. This 3-dimensional analogue of the moduli space M(S) of unmarked hyperbolic surfaces homeomorphic to S has bizarre local topology, possessing many points that are not closed. There is, however, a natural embedding of M(S) into AI(S) and a compactification of AI(S) such that this embedding extends to an embedding of the Deligne-Mumford compactification of M(S) into the compactification of AI(S).

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