International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 4, Pages 251-255
doi:10.1155/S0161171200003379
Local subhomeotopy groups of bounded surfaces
Department of Mathematical Sciences, Villanova University, Villanova, 19085, PA, USA
Received 2 February 1999; Revised 10 May 1999
Copyright © 2000 David J. Sprows. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.