Richiamo il seminario di geometria domani alle 15.
(Purtroppo io, Leone ed alcuni studenti siamo ad una conferenza e non ci saremo -- Lo speaker è qui a Pisa solo questa settimana, ospite di Giulio Belletti, e non c'era altra soluzione.)
A presto,
  Bruno

On Thu, Jun 20, 2019 at 10:34 AM Bruno Martelli <martelli@dm.unipi.it> wrote:
Buondì,

Segnalo un seminario di geometria per mercoledì prossimo alle 15. 
A presto,
  Bruno

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26-Jun-2019 15:00
On type-preserving representations of the four-punctured sphere group
Tian Yang
Texas A&M University

We give counterexamples to a conjecture of Bowditch that if a non-elementary type-preserving representation ρ : π1(Σg,n) → P SL(2; R) of a punctured surface group sends every non-peripheral simple closed curve to a hyperbolic element, then ρ must be Fuchsian. The counterexamples come from relative Euler class
±1 representations of the four-punctured sphere group. As a related result, we show that the mapping class group action on each non-extremal component of the character space of type-preserving representations of the four-punctured sphere
group is ergodic, confirming a conjecture of Goldman in this case. The main tool we use is the lengths coordinates of the decorated character spaces defined by Kashaev. At the end of the talk, I will also mention a recent joint work with Sara Maloni and Frederic Palesi on representations of the three-punctured projective
plane group.