Difference between revisions of "Simple space"
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* {{booklink|Concise}}, Page 140 (formal definition) | * {{booklink|Concise}}, Page 140 (formal definition) | ||
* {{booklink|Hatcher}}, Page 342 (definition in paragraph): Hatcher uses the term '''Abelian space''' locally in the book | * {{booklink|Hatcher}}, Page 342 (definition in paragraph): Hatcher uses the term '''Abelian space''' locally in the book | ||
− | * {{booklink|Spanier}}, Page 384 ( | + | * {{booklink|Spanier}}, Page 384 (definition in paragraph) |
Revision as of 21:59, 21 April 2008
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)