Invariant spanning trees for quadratic rational maps

Abstract

We study Thurston equivalence classes of quadratic post-critically finite branched coverings. For these maps, we introduce and study invariant spanning trees. We give a computational procedure for searching for invariant spanning trees. This procedure uses bisets over the fundamental group of a punctured sphere. We also introduce a new combinatorial invariant of Thurston classes - the ivy graph.

A small but essential correction in Theorem A compared to the published version; 55 pages, 8 figures