"Harmonic measure and rigidity for surface group actions on the circle"Adachi, MasanoriIn 1990s, Frankel and Thurston independently proposed alternative proofs for the Milnor-Wood inequality based on foliated harmonic measures. In particular, Frankel pointed out that Matsumoto's rigidity theorem directly follows from his argument. Revisiting their approach, we shall give a harmonic measure proof for a theorem of Burger, Iozzi and Weinhard: a Milnor-Wood type inequality and a Matsumoto type rigidity theorem for actions of torsion-free, but not necessarily cocompact, lattices of $\operatorname{PSL}(2;\mathbb{R})$ on the circle. This is joint work with Yoshifumi Matsuda (Aoyama Gakuin University) and Hiraku Nozawa (Ritsumeikan University). |
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