Canonical decomposition of rational maps

Abstract: There are various classical and more recent decomposition results in mapping class group theory, geometric group theory, and complex dynamics (which include celebrated results by Bill Thurston). The goal of this talk is to introduce a powerful decomposition of rational maps based on the topological structure of their Julia sets. Namely, we will discuss the following result: every postcritically-finite rational map with non-empty Fatou set can be canonically decomposed into crochet maps (these have very "thinly connected" Julia sets) and Sierpinski carpet maps (these have very "heavily connected" Julia sets). If time permits, I will discuss applications of this result in various aspects of geometric group theory.

This is based on joint work with Dima Dudko and Dierk Schleicher.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

( paper | slides )

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Geometry and topology online

Series comments: You can also find up-to-date information on the seminar homepage - warwick.ac.uk/fac/sci/maths/research/events/seminars/areas/geomtop/

The talks start at 13:30. Talks are typically fifty minutes long, with ten minutes for questions.

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