Local subhomeotopy groups of bounded surfaces

Abstract

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.

Keywords

• Local subhomeotopy group
• isotopy class
• twist homeomorphism
• spin homeomorphism.