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}
}
Comments
15 pages