Abstract
In this thesis we prove rational homological stability for the classifying spaces of the homotopy automorphisms and block di↵eomorphisms of iterated connected sums of products of spheres of a certain connectivity.The results in particular apply to the manifolds
Npg,q = (#g(Sp x Sq)) - int(Dp+q) , where 3 ≤ p < q < 2p − 1.
We show that the homology groups
H*(Baut∂(Npg,q );Q) and H*(BDiffNpg,q(Npg,q);Q)
are independent of g for ∗< g/2−1. To prove the homological stability for the homotopy automorphisms we show that the groups π1(Baut∂(Npg,q )) satisfy homological stability with coefficients in the homology of the universal covering, which is studied using rational homology theory. The result for the block di↵eomorphisms is deduced from the homological stability for the homotopy automorphisms upon using Surgery theory. Themain theorems of this thesis extend the homological stability results in [BM15] where the automorphism spaces of (Npg,q ) are studied.
Npg,q = (#g(Sp x Sq)) - int(Dp+q) , where 3 ≤ p < q < 2p − 1.
We show that the homology groups
H*(Baut∂(Npg,q );Q) and H*(BDiffNpg,q(Npg,q);Q)
are independent of g for ∗< g/2−1. To prove the homological stability for the homotopy automorphisms we show that the groups π1(Baut∂(Npg,q )) satisfy homological stability with coefficients in the homology of the universal covering, which is studied using rational homology theory. The result for the block di↵eomorphisms is deduced from the homological stability for the homotopy automorphisms upon using Surgery theory. Themain theorems of this thesis extend the homological stability results in [BM15] where the automorphism spaces of (Npg,q ) are studied.
| Original language | English |
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| Publisher | Department of Mathematical Sciences, Faculty of Science, University of Copenhagen |
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| Number of pages | 79 |
| ISBN (Print) | 978-87-7078-956-1 |
| Publication status | Published - 2015 |