Homological stability of diffeomorphism groups

2012/03/19 by Alexander Berglund, Berglund, Alexander, Ib Madsen +1
Mathematics · #55P62 #57R50 #57R65 #57S05 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #math.AT #math.GT #msc:55P62 #msc:57R50 #msc:57R65 #msc:57S05

paper · pdf · doi:10.48550/arxiv.1203.4161

31 pages; minor corrections; added references

arxiv created 2012/09/04 · arxiv updated 2012/09/05

Abstract

In this paper we prove a stability theorem for block diffeomorphisms of 2d-dimensional manifolds that are connected sums of S^d x S^d. Combining this with a recent theorem of S. Galatius and O. Randal-Williams and Morlet's lemma of disjunction, we determine the homology of the classifying space of their diffeomorphism groups relative to an embedded disk in a stable range.

Related

• Homological stability of diffeomorphism groups of high dimensional manifolds via E_k-algebras
• Proving homological stability for homeomorphisms of manifolds
• Homological stability and stable moduli of flat manifold bundles
• Homological stability for moduli spaces of high dimensional manifolds
• A remark on stability and the D-topology of mapping spaces