PUB - Publikationen an der Universität Bielefeld

For every n ≥ 2, the surface Houghton group Bn is defined as the asymptotically rigid mapping class group of a surface with exactly n ends, all of them non-planar. The groups Bn are analogous to, and in fact contain, the braided Houghton groups. These groups also arise naturally in topology: every monodromy homeomorphism of a fibered component of a depth-1 foliation of closed 3-manifold is conjugate into some Bn . As countable mapping class groups of infinite type surfaces, the groups Bn lie somewhere between classical mapping class groups and big mapping class groups. We initiate the study of surface Houghton groups proving, among other things, that Bn is of type Fn−1 , but not of type FPn , analogous to the braided Houghton groups.