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Peter Storm

Publications and source records attributed to Peter Storm.

5 recordsLinked to original sources
arXiv2010

The curious moduli spaces of unmarked Kleinian surface groups

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).

math.GT↗
arXiv2009

Dense embeddings of surface groups

We discuss dense embeddings of surface groups and fully residually free groups in topological groups. We show that a compact topological group contains a nonabelian dense free group of finite rank if and only if it contains a dense surface group. Also, we obtain a characterization of those Lie groups which admit a dense faithfully embedded surface group. Similarly, we show that any connected semisimple Lie group contains a dense copy of any fully residually free group.

math.GR↗
arXiv2009

Dynamics of the mapping class group action on the variety of PSL(2,C) characters

We study the action of the mapping class group Mod(S) on the boundary dQ of quasifuchsian space Q. Among other results, Mod(S) is shown to be topologically transitive on the subset C in dQ of manifolds without a conformally compact end. We also prove that any open subset of the character variety X(pi_1(S),SL(2,C)) intersecting dQ does not admit a nonconstant Mod(S)-invariant meromorphic function. This is related to a question of Goldman.

math.GT↗
arXiv2005

Finitely generated subgroups of lattices in PSL(2,C)

Let G be a lattice in PSL(2,C). The pro-normal topology on G is defined by taking all cosets of non-trivial normal subgroups as a basis. This topology is finer than the pro-finite topology, but it is not discrete. We prove that every finitely generated subgroup H<G is closed in the pro-normal topology. As a corollary we deduce that if M is a maximal subgroup of a lattice in PSL(2,C) then either M is finite index or M is not finitely generated.

math.GT↗