Given a family of groups admitting a braided monoidal structure (satisfying mild
assumptions) we construct a family of spaces on which the groups act and whose …

We prove an analogue of the Madsen–Weiss theorem for high-dimensional manifolds. In
particular, we explicitly describe the ring of characteristic classes of smooth fibre bundles …

This is an exposition of homotopical results on the geometric realisation of semisimplicial
spaces. We then use these to derive basic foundational results about classifying spaces of …

We prove a homological stability theorem for families of discrete groups (eg mapping class
groups, automorphism groups of free groups, braid groups) with coefficients in a sequence …

We prove a homological stability theorem for moduli spaces of manifolds of dimension 2n,
for attaching handles of index at least n, after these manifolds have been stabilised by …

We prove that the braided Thompson's groups V br and F br are of type F∞, confirming a
conjecture by John Meier. The proof involves showing that matching complexes of arcs on …

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 …

We determine $\pi _*(B\operatorname {Diff} _\partial (D^{2n}))\otimes\mathbb {Q} $ for $2
n\geq 6$ completely in degrees $*\leq 4n-10$, far beyond the pseudoisotopy stable range …

The Pontryagin classes of an m–dimensional real vector bundle satisfy well-known
vanishing relations due to their close relationship with the Chern classes of the complexified …

We construct infinite rank summands isomorphic to $\mathbb {Z}^\infty $ in the higher
homotopy and homology groups of the diffeomorphism groups of certain $4 $-manifolds …