Space with perfect fundamental group

This article defines a homotopy-invariant property of topological spaces, i.e. a property of homotopy classes of topological spaces

View other homotopy-invariant properties of topological spaces OR view all properties of topological spaces

This property of topological spaces is defined as the property of the following associated group: fundamental group having the following group property: perfect group

This property of topological spaces is defined as the property of the following associated group: first homology group having the following group property: trivial group

Definition

A topological space is said to have perfect fundamental group if it satisfies the following equivalent conditions:

• It is path-connected, and its fundamental group is perfect
• It is path-connected, and the first homology group is trivial

Relation with other properties

Stronger properties

• Simply connected space
• Acyclic space