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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.
Hatcher, Allen 1 ; McCullough, Darryl 2
@article{GT_1997_1_1_a6, author = {Hatcher, Allen and McCullough, Darryl}, title = {Finiteness of classifying spaces of relative diffeomorphism groups of 3{\textendash}manifolds}, journal = {Geometry & topology}, pages = {91--109}, publisher = {mathdoc}, volume = {1}, number = {1}, year = {1997}, doi = {10.2140/gt.1997.1.91}, url = {http://geodesic.mathdoc.fr/articles/10.2140/gt.1997.1.91/} }
TY - JOUR AU - Hatcher, Allen AU - McCullough, Darryl TI - Finiteness of classifying spaces of relative diffeomorphism groups of 3–manifolds JO - Geometry & topology PY - 1997 SP - 91 EP - 109 VL - 1 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/gt.1997.1.91/ DO - 10.2140/gt.1997.1.91 ID - GT_1997_1_1_a6 ER -
%0 Journal Article %A Hatcher, Allen %A McCullough, Darryl %T Finiteness of classifying spaces of relative diffeomorphism groups of 3–manifolds %J Geometry & topology %D 1997 %P 91-109 %V 1 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/gt.1997.1.91/ %R 10.2140/gt.1997.1.91 %F GT_1997_1_1_a6
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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