Aspherical manifolds
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| − | + | A path-connected space $X$ is called aspherical is its higher homotopy groups vanish: $\pi_i(X) = 0$ for all $i \geq 2$. This article is about closed, aspherical manifolds $M$ which are connected manifolds with contractible universal cover $\widetilde M \simeq *$. | |
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Revision as of 11:50, 30 November 2009
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An earlier version of this page was published in the Bulletin of the Manifold Atlas: screen, print. You may view the version used for publication as of 12:23, 27 September 2012 and the changes since publication. |
Contents |
1 Introduction
A path-connected space 
is called aspherical is its higher homotopy groups vanish: 
for all 
. This article is about closed, aspherical manifolds 
which are connected manifolds with contractible universal cover 
.
2 Construction and examples
3 Invariants
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4 Classification/Characterization (if available)
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5 Further discussion
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6 References
- [Farrell&Jones1990] F. T. Farrell and L. E. Jones, Classical aspherical manifolds, Published for the Conference Board of the Mathematical Sciences, Washington, DC, 1990. MR1056079 (91k:57001) Zbl 0729.57001
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This page has not been refereed. The information given here might be incomplete or provisional. |
