Rational Homological Stability for Automorphisms of Manifolds

Publikation: Bog/antologi/afhandling/rapportPh.d.-afhandling

  • Matthias Grey
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.
OriginalsprogEngelsk
ForlagDepartment of Mathematical Sciences, Faculty of Science, University of Copenhagen
Antal sider79
ISBN (Trykt)978-87-7078-956-1
StatusUdgivet - 2015

ID: 147658448