KTH/SU Mathematics Colloquium
December 2, 2009
Laurent Bartholdi, Georg-August University of Göttingen
Insanely twisted rabbits
(Topological) branched coverings of the sphere, modulo a natural
("isotopy") relation, are interesting combinatorial objects; and a
result by Thurston explains, at least theoretically, when such a
covering is equivalent to a rational map.
I will explain how such coverings can be conveniently encoded in group
theory, and how that language can be used to answer a long-standing
open problem by Douady and Hubbard, the "Twisted rabbit problem".
I will then discuss visualizations of "matings" of polynomials (the
topological branched covering obtained from gluing together two
polynomials at infinity) through the same method.
This is joint work with Volodya Nekrashevych.