Geometry & Topology
- Geom. Topol.
- Volume 1, Number 1 (1997), 91-109.
Finiteness of classifying spaces of relative diffeomorphism groups of 3–manifolds
The main theorem shows that if is an irreducible compact connected orientable 3–manifold with non-empty boundary, then the classifying space of the space of diffeomorphisms of which restrict to the identity map on has the homotopy type of a finite aspherical CW–complex. This answers, for this class of manifolds, a question posed by M Kontsevich. The main theorem follows from a more precise result, which asserts that for these manifolds the mapping class group is built up as a sequence of extensions of free abelian groups and subgroups of finite index in relative mapping class groups of compact connected surfaces.
Geom. Topol., Volume 1, Number 1 (1997), 91-109.
Received: 12 June 1997
Revised: 19 December 1997
First available in Project Euclid: 21 December 2017
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Hatcher, Allen; McCullough, Darryl. Finiteness of classifying spaces of relative diffeomorphism groups of 3–manifolds. Geom. Topol. 1 (1997), no. 1, 91--109. doi:10.2140/gt.1997.1.91. https://projecteuclid.org/euclid.gt/1513882847