International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 4, Pages 251-255

Local subhomeotopy groups of bounded surfaces

David J. Sprows

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.


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.