Let Mn denote the 2-dimensional manifold with
boundary obtained by removing the interiors of n
disjoint closed disks from a closed 2-manifold M and
let Mn,r denote the manifold obtained by removing
r distinct points from the interior of Mn.
The subhomeotopy group of Mn,r, denoted
Hn(Mn,r), is defined to be the group of all
isotopy classes (rel ∂Mn,r) of
homeomorphisms of Mn,r that are the identity on
the boundary. In this paper, we use the isotopy classes of
various homeomorphisms of Sn+1,r2 to investigate
the subgroup of Hn(Mn,r) consisting of those
elements that are presented
by local homeomorphisms.