Pure and Applied Mathematics Quarterly
Volume 9 (2013)
Special Issue: In Honor of Dennis Sullivan, Part 1 of 2
Homological stability of diffeomorphism groups
Pages: 1 – 48
In this paper we prove a stability theorem for block diffeomorphisms of $2d$-dimensional manifolds that are connected sums of $S^d \times S^d$. 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.
algebraic topology of manifolds, rational homotopy theory, block bundles