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We study stable commutator length on mapping class groups of certain infinite-type surfaces. In particular, we show that stable commutator length defines a continuous function on the commutator subgroups of such infinite-type mapping class groups. We furthermore show that the commutator subgroups are open and closed subgroups and that the abelianizations are finitely generated in many cases. Our results apply to many popular infinite-type surfaces with locally coarsely bounded mapping class groups.
We give a new upper bound on the stable commutator length of Dehn twists in hyperelliptic mapping class groups, and determine the stable commutator length of some elements. We also calculate values and the defects of homogeneous quasimorphisms derive
Let $Gamma$ be a finite index subgroup of the mapping class group $MCG(Sigma)$ of a closed orientable surface $Sigma$, possibly with punctures. We give a precise condition (in terms of the Nielsen-Thurston decomposition) when an element $ginGamma$ ha
We study the action of (big) mapping class groups on the first homology of the corresponding surface. We give a precise characterization of the image of the induced homology representation.
We give an algorithm to compute stable commutator length in free products of cyclic groups which is polynomial time in the length of the input, the number of factors, and the orders of the finite factors. We also describe some experimental and theoretical applications of this algorithm.
We give a new proof of a theorem of D. Calegari that says that the Cayley graph of a surface group with respect to any generating set lying in finitely many mapping class group orbits has infinite diameter. This applies, for instance, to the generating set consisting of all simple closed curves.