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1997 Finiteness of classifying spaces of relative diffeomorphism groups of 3–manifolds
Allen Hatcher, Darryl McCullough
Geom. Topol. 1(1): 91-109 (1997). DOI: 10.2140/gt.1997.1.91


The main theorem shows that if M is an irreducible compact connected orientable 3–manifold with non-empty boundary, then the classifying space BDiff(MrelM) of the space of diffeomorphisms of M which restrict to the identity map on M 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 (MrelM) 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.


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Allen Hatcher. Darryl McCullough. "Finiteness of classifying spaces of relative diffeomorphism groups of 3–manifolds." Geom. Topol. 1 (1) 91 - 109, 1997.


Received: 12 June 1997; Revised: 19 December 1997; Published: 1997
First available in Project Euclid: 21 December 2017

zbMATH: 0885.57008
MathSciNet: MR1486644
Digital Object Identifier: 10.2140/gt.1997.1.91

Primary: 57M99
Secondary: 55R35 , 58D99

Keywords: 3–manifold , classifying space , diffeomorphism , geometrically finite , homeotopy group , mapping class group , torsion

Rights: Copyright © 1997 Mathematical Sciences Publishers


Vol.1 • No. 1 • 1997
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