Fragmentation norm and relative quasimorphisms Academic Article uri icon

abstract

  • Homeomorphisms of a connected manifold M can be often expressed as compositions of homeomorphisms supported in sets of a given cover of M. This is known as the fragmentation property. In this paper we are interested in groups G ⊆ Homeo0(M,µ) of compactly supported measure-preserving homeomorphisms which satisfy the fragmentation property with respect to topological balls of measure at most one. Given f ∈ G, its fragmentation norm ffrag is defined to be the smallest n such that f = g1 ···gn and each gi is supported in a ball of measure at most one. Thus the fragmentation norm is the word norm on G associated with the generating set consisting of maps supported in balls as above. We are also interested in the stable fragmentation … The main result of the paper provides conditions under which the exis- tence of an essential quasimorphism (see Section 2.1) on the fundamen- tal group of M implies the existence of an element of G with a positive

publication date

  • January 1, 2018