English

The curious moduli spaces of unmarked Kleinian surface groups

Geometric Topology 2010-08-03 v2

Abstract

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).

Keywords

Cite

@article{arxiv.0906.5601,
  title  = {The curious moduli spaces of unmarked Kleinian surface groups},
  author = {Richard Canary and Peter Storm},
  journal= {arXiv preprint arXiv:0906.5601},
  year   = {2010}
}

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15 pages