University of Cambridge > Talks.cam > Differential Geometry and Topology Seminar > Fixed point theorems for holomorphic maps on Teichmueller spaces and beyond

Fixed point theorems for holomorphic maps on Teichmueller spaces and beyond

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  • UserStergios Antonakoudis, Cambridge
  • ClockWednesday 20 January 2016, 16:00-17:00
  • HouseMR13.

If you have a question about this talk, please contact Ivan Smith.

Studying the existence of fixed points for holomorphic maps on Teichm\”uller spaces serves as a framework for proving ‘geometrization’ theorems, such as Thurston’s topological characterisation of hyperbolic 3-manifolds. In this talk, we will prove a general theorem addressing the question of existence of fixed points for holomorphic maps on Teichmueller spaces and on a more general class of complex domains by focusing our study on the intrinsic geometry of the domains. Finally, we will also deduce an analogous topological result generalising the theorem, by leveraging a simple combinatorial idea from Ramsey theory to bypass the use of complex analysis in the proof.

This talk is part of the Differential Geometry and Topology Seminar series.

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