Space with Abelian mapping class group
This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces
This property of topological spaces is defined as the property of the following associated group: mapping class group having the following group property: Abelian group
Definition
A topological space is said to have Abelian mapping class group if its mapping class group is Abelian.
Relation with other properties
Stronger properties
Facts
In a space with Abelian mapping class group, any two conjugate self-homeomorphisms are isotopic, and hence, in particular, homotopic. Thus, the problem of finding a good self-homeomorphism that is conjugate to an arbitrary self-homeomorphism, also solves the problem of finding a good self-homeomorphism that is homotopy-equivalent to the given one.