Boundary Fixed Homeomorphisms of 2-Manifolds with Boundary

Abstract

Let X be a closed, orientable 2-manifold and let n X denote the bounded manifold obtained by removing the interiors of n disjoint closed disks from X .Let ( ) n H X denote the group of isotopy classes (rel boundary of n X ) of homeomorphisms of n X which are the identity on the boundary of n X . ( ) n H X has been determined for all n when X is the 2-sphere (see [8] and [10]). This paper investigates the structure of ( ) n H X for X not equal to the 2-sphere. In particular, a relationship between ( ) n H X and the homeotopy group (mapping class group)of X (see [4],[5]and [11]) is developed.