We prove a homological stability theorem for moduli spaces of simply connected manifolds
of dimension $2 n> 4$, with respect to forming connected sum with $ S^ n\times S^ n $. This …

We study the homotopy type of the space of metrics of positive scalar curvature on high-
dimensional compact spin manifolds. Hitchin used the fact that there are no harmonic …

Building on work of Stolz, we prove for integers $0\le d\le 3$ and $ k> 232$ that the
boundaries of $(k-1) $-connected, almost closed $(2k+ d) $-manifolds also bound …

We prove that in dimension≠ 4, 5, 7 the homology and homotopy groups of the classifying
space of the topological group of diffeomorphisms of a disk fixing the boundary are finitely …

The study of manifolds and invariants of manifolds was begun more than a century ago. In
this entry we shall discuss the parametrised setting: invariants of families of manifolds …

We compute the mapping class group of the manifolds ♯^ g (S^ 2k+ 1 * S^ 2k+ 1)♯ g (S 2
k+ 1× S 2 k+ 1) for k> 0 k> 0 in terms of the automorphism group of the middle homology and …

In 1962, Wall showed that smooth, closed, oriented, $(n-1) $-connected $2 n $-manifolds of
dimension at least $6 $ are classified up to connected sum with an exotic sphere by an …

Motivated by the operad built from moduli spaces of Riemann surfaces, we consider a
general class of operads in the category of spaces that satisfy certain homological stability …

Abstract We prove the Farrell–Jones conjecture for (nonconnective) A–theory with
coefficients and finite wreath products for hyperbolic groups, CAT (0)–groups, cocompact …

It is well known that Sullivan showed that the mapping class group of a simply connected
highdimensional manifold is commensurable with an arithmetic group, but the meaning of …