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Harmonic measures and
rigidity for surface group actions on the circle
Masanori Adachi, Yoshifumi Matsuda and Hiraku Nozawa |
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Algebraic & Geometric Topology 25 (2025) 2391–2412
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Abstract |
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We study rigidity properties of actions of a torsion-free lattice of on the circle . We follow the approaches of Frankel and Thurston proposed in preprints via foliated harmonic measures on the suspension bundles. Our main results are a curvature estimate and a Gauss–Bonnet formula for the connection obtained by taking the average of the flat connection with respect to a harmonic measure. As consequences, we give a precise description of the harmonic measure on suspension foliations with maximal Euler number and an alternative proof of rigidity theorems of Matsumoto and Burger, Iozzi and Wienhard. |
Keywords
group action, surface group, Euler number, harmonic
measure, Gauss–Bonnet formula, rigidity
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Mathematical Subject Classification
Primary: 22D50, 53C12
Secondary: 31A15, 57M60, 57R20, 58D19
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References |
Publication
Received: 1 October 2023
Revised: 15 April 2024
Accepted: 12 May 2024
Published: 11 August 2025
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Authors |
| Masanori Adachi | |
| Department of Mathematics Shizuoka University Shizuoka Japan |
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| Yoshifumi Matsuda | |
| Department of Mathematical
Sciences Aoyama Gakuin University Sagamihara Japan |
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| Hiraku Nozawa | |
| Department of Mathematical
Sciences Ritsumeikan University Kusatsu Japan |
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| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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