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
.
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