Quasi-homomorphisms and stable lengths in mapping class groups

Abstract

We give elementary applications of quasi-homomorphisms to growth problems in groups. A particular case concerns the number of torsion elements required to factorise a given element in the mapping class group of a surface.

Revised to include a discussion of weak bounded generation, both in general and for mapping class groups; now 8 pages

Cited by in corpus (8)

• Geometry of pseudocharacters
• On bi-invariant word metrics
• Higher-order signature cocycles for subgroups of mapping class groups and homology cylinders
• Actions of certain arithmetic groups on Gromov hyperbolic spaces
• On the commutator length of a Dehn twist
• Failure of separation by quasi-homomorphisms in mapping class groups
• Signatures of surface bundles and stable commutator lengths of Dehn twists
• Cosmetic two-strand twists on fibered knots