TY - BOOK

T1 - Rational Homological Stability for Automorphisms of Manifolds

AU - Grey, Matthias

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

UR - https://soeg.kb.dk/permalink/45KBDK_KGL/fbp0ps/alma99122158630005763

M3 - Ph.D. thesis

SN - 978-87-7078-956-1

BT - Rational Homological Stability for Automorphisms of Manifolds

PB - Department of Mathematical Sciences, Faculty of Science, University of Copenhagen

ER -