Dynamics of the mapping class group action on the variety of PSL(2,C) characters
Abstract
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(pi1(S),SL(2,C)) intersecting dQ does not admit a nonconstant Mod(S)-invariant meromorphic function. This is related to a question of Goldman.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.