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Local subhomeotopy groups of bounded surfaces. (English) Zbl 0966.57026

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.

MSC:

57N37 Isotopy and pseudo-isotopy
57N05 Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010)
57P05 Local properties of generalized manifolds
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