Using Spin, Twist and Dial Homeomorphisms to Generate Homeotopy Groups
In this paper we consider some problems concerned with the isotopy classification of homeomorphisms of multiply punctured compact 2-manifolds, i.e., manifolds of the form X – ∪ m i=1 Definitions and Notation D̊ i – Pwhere X is a closed 2-manifold, {Di :1<i<m} is a family of disjoint discs in X and P = {pm+1, …, pn} is a finite subset of X disjoint from each Di. Inparticular we will show that various homeotopy groups for these manifolds are generated by the isotopy class of three types of homeomorphisms. In the case X is the two sphere we will give a complete presentation of these homeotopy groups. Parts of the material in this paper have been considered in [5 ], [6] and [7], but this is the first time that a full treatment of this topic, including detailed illustrations of the isotopies involved, has been submitted for publication. For an alternate approach to the material in this paper see (for example) [2], and [].
