Finiteness of classifying spaces of relative diffeomorphism groups of 3–manifolds
Geometry & topology, Tome 1 (1997) no. 1, pp. 91-109.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/gt.1997.1.91
Keywords: 3–manifold, diffeomorphism, classifying space, mapping class group, homeotopy group, geometrically finite, torsion

Hatcher, Allen 1 ; McCullough, Darryl 2

1 Department of Mathematics, Cornell University, Ithaca, New York 14853, USA
2 Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019, USA
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Hatcher, Allen; McCullough, Darryl. Finiteness of classifying spaces of relative diffeomorphism groups of 3–manifolds. Geometry & topology, Tome 1 (1997) no. 1, pp. 91-109. doi : 10.2140/gt.1997.1.91. http://geodesic.mathdoc.fr/articles/10.2140/gt.1997.1.91/

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