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Thurston Theory: Connecting Geometry, Topology and Complex Dynamics

[HYBRID WORKSHOP] Connections Workshop: Complex Dynamics - from special families to natural generalizations in one and several variables February 02, 2022 - February 04, 2022

February 02, 2022 (11:30 AM PST - 11:55 AM PST)
Speaker(s): Rebecca Winarski (College of the Holy Cross; MSRI - Mathematical Sciences Research Institute)
Location: MSRI: Simons Auditorium, Online/Virtual
Tags/Keywords
  • Thurston theory

  • mapping class groups

  • branched covers

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Thurston Theory: Connecting Geometry, Topology And Complex Dynamics

Abstract

Thurston proved that a non-Lattés branched cover of the sphere to itself is either equivalent to a rational map (that is: conjugate via a mapping class), or has a topological obstruction. The Nielsen–Thurston classification of mapping classes is an analogous theorem in low-dimensional topology. We unify these two theorems with a single proof, further connecting techniques from surface topology and complex dynamics. This is joint work with Jim Belk and Dan Margalit.

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Thurston Theory: Connecting Geometry, Topology And Complex Dynamics

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