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 …

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 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 …

We study the $\mathscr {D}\mathrm {isc} $-structure space $ S^{\mathscr {D}\mathrm {isc}}
_\partial (M) $ of a compact smooth manifold M. Informally speaking, this space measures …

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 …

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 …

Given a graded E 1–module over an E 2–algebra in spaces, we construct an augmented
semi-simplicial space up to higher coherent homotopy over it, called its canonical resolution …

We compute the rational homotopy groups in degrees up to approximately $\tfrac {3}{2} $ d
of the group of diffeomorphisms of a closed d-dimensional disc fixing the boundary. Based …

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 …

ON THE COHOMOLOGY OF TORELLI GROUPS Page 1 Forum of Mathematics, Pi (2020),
Vol. 8, e7, 83 pages doi:10.1017/fmp.2020.5 1 ON THE COHOMOLOGY OF TORELLI …