Duke Mathematical Journal
- Duke Math. J.
- Volume 131, Number 3 (2006), 441-468.
Distortion elements in group actions on surfaces
If is a finitely generated group with generators , then an infinite-order element is a distortion element of provided that where is the word length of in the generators. Let be a closed orientable surface, and let denote the identity component of the group of -diffeomorphisms of . Our main result shows that if has genus at least two and that if is a distortion element in some finitely generated subgroup of , then for every -invariant Borel probability measure . Related results are proved for or . For a Borel probability measure on , denote the group of -diffeomorphisms that preserve by . We give several applications of our main result, showing that certain groups, including a large class of higher-rank lattices, admit no homomorphisms to with infinite image
Duke Math. J., Volume 131, Number 3 (2006), 441-468.
First available in Project Euclid: 6 February 2006
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 37C85: Dynamics of group actions other than Z and R, and foliations [See mainly 22Fxx, and also 57R30, 57Sxx]
Secondary: 57M60: Group actions in low dimensions 22F10: Measurable group actions [See also 22D40, 28Dxx, 37Axx]
Franks, John; Handel, Michael. Distortion elements in group actions on surfaces. Duke Math. J. 131 (2006), no. 3, 441--468. doi:10.1215/S0012-7094-06-13132-0. https://projecteuclid.org/euclid.dmj/1139232346