Homological stability of diffeomorphism groups of high dimensional manifolds via Ek-algebras
Abstract
We will study homological stability of the diffeomorphism groups of the manifolds $W_{g,1}:=D^{2n} \# (S^n \times S^n)^{\#g }$ using $E_k$-algebras. This will lead to new improvements in the stability results, especially when working with rational coefficients. Moreover, we will prove a new type of stability result -- quantised homological stability -- which says that either the best stability result is a linear bound of slope $1/2$ or the stability is at least as good as a line of slope $2/3$.
Fields of Study & Subjects
Alcoholism and Thiamine Deficiency
Homotopy and Cohomology in Algebraic Topology
Amino Acid Enzymes and Metabolism
Publication details
- Journal / source
- Advances in Mathematics
- Volume
- 497
- Pages
- 110994–110994
- Publication date
- 8 May 2026
- Language
- EN