Local subhomeotopy groups of bounded surfaces
The subgroup consisting of elements presented by local homeomorphisms of the so-called subhomeotopy group, denoted by \(H_n(M_{n,r})\) of a 2-dimensional manifold \(M_{n,r}\), obtained by removing the interiors of \(n\) disjoint closed disks and \(r\) distinct points from the interior of the obtained manifold, is discussed by making use of the isotopy classes of various homeomorphisms of \(S^2_{n+1,r}\). It is shown that there are three types of generating sets for this subgroup and the commutator relations for the generators are given. Depending on the manifold and on the value of \(n\), the number of generators can be reduced.
scientific article; zbMATH DE number 1533319