Simple space
This article defines a homotopy-invariant property of topological spaces, i.e. a property of homotopy classes of topological spacesView other homotopy-invariant properties of topological spaces OR view all properties of topological spaces
Contents
Definition
A topological space is termed simple if it satisfies the following three conditions:
- It is path-connected
- The fundamental group is Abelian
- The fundamental group acts trivially on all the higher homotopy groups
Relation with other properties
Stronger properties
- Simply connected space
- Aspherical space with Abelian fundamental group
Weaker properties
References
Textbook references
- A Concise Course in Algebraic Topology by J Peter May^{Full text PDF}^{More info}, Page 140 (formal definition)
- Algebraic Topology by Allen Hatcher^{Full text PDF}^{More info}, Page 342 (definition in paragraph): Hatcher uses the term Abelian space locally in the book
- Algebraic Topology by Edwin H. Spanier^{More info}, Page 384 (definition in paragraph)