STABLE COMMUTATOR LENGTHIS RATIONAL IN FREE GROUPS

摘要

Stable commutator length is a numerical invariant of elements in the commu-tator subgroup of a group. It is intimately related to (two-dimensional) boundedcohomology and appears in many areas of low-dimensional topology and dynamics,from the Milnor-Wood inequality, to the 11/8 conjecture. However, although agreat deal of work has gone into estimating or bounding stable commutator lengthin many contexts, there are very few known nontrivial examples of finitely presentedgroups in which it can be calculated exactly, and virtually no cases where the rangeof stable commutator length on a given group can be understood arithmetically.