We prove a homological stability theorem for the diffeomorphism groups of high-dimensional manifolds with boundary, with respect to forming the boundary connected sum with the product for . In a recent joint paper with B Botvinnik, we prove that there is an isomorphism
in the case that . By combining this “stable homology” calculation with the homological stability theorem of this paper, we obtain the isomorphism
in the case that .
"Homological stability for diffeomorphism groups of high-dimensional handlebodies." Algebr. Geom. Topol. 18 (5) 2769 - 2820, 2018. https://doi.org/10.2140/agt.2018.18.2769