Related papers: Diffeomorphism groups of solid tori and the ration…

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 on this we determine the optimal rational concordance stable…

For a compact $(2n+1)$-dimensional smooth manifold, let $\mu_M : B Diff_\partial (D^{2n+1}) \to B Diff (M)$ be the map that is defined by extending diffeomorphisms on an embedded disc by the identity. By a classical result of Farrell and…

We determine $\pi_*(BDiff_\partial(D^{2n})) \otimes \mathbb{Q}$ for $2n \geq 6$ completely in degrees $* \leq 4n-10$, far beyond the pseudoisotopy stable range. Furthermore, above these degrees we discover a systematic structure in these…

In this paper 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 $D^{p+1}\times S^{q}$ for $|q - p| <…

We study the infinite generation in the homotopy groups of the group of diffeomorphisms of $S^1 \times D^{2n-1}$, for $2n \geq 6$, in a range of degrees up to $n-2$. Our analysis relies on understanding the homotopy fibre of a linearisation…

I describe what is currently known, for $d \geq 5$, about the rational homotopy type of the group of diffeomorphisms of the $d$-disc relative to its boundary, and the closely related group of homeomorphisms of $d$-dimensional Euclidean…

We study the rational homotopy types of classifying spaces of automorphism groups of smooth simply connected manifolds of dimension at least five. We give dg Lie algebra models for the homotopy automorphisms and the block diffeomorphisms of…

We calculate the rational cohomology of the classifying space of the diffeomorphism group of the manifolds $U_{g,1}^n:= \#^g(S^n \times S^{n+1})\setminus \mathrm{int}{D^{2n+1}}$, for large $g$ and $n$, up to approximately degree $n$. The…

We study the moduli space of handlebodies diffeomorphic to $(D^{n+1}\times S^{n})^{\natural g}$, i.e. the classifying space $BDiff((D^{n+1}\times S^n)^{\natural g}, D^{2n})$ of the group of diffeomorphisms that restrict to the identity near…

We construct a zig-zag from the once delooped space of pseudoisotopies of a closed $2n$-disc to the once looped algebraic $K$-theory space of the integers and show that the maps involved are $p$-locally $(2n-4)$-connected for $n>3$ and…

In this paper we prove a stability theorem for block diffeomorphisms of 2d-dimensional manifolds that are connected sums of S^d x S^d. Combining this with a recent theorem of S. Galatius and O. Randal-Williams and Morlet's lemma of…

This paper provides a diffeomorphism classification of smooth manifolds homeomorphic to the complex projective space $\mathbb{C}P^m$ for $m \in \{5, 6, 7, 8\}$. The classification is obtained by computing the group of concordance classes of…

Smooth structures on high dimensional manifolds are classified by maps to the infinite loop space $TOP/O$. The homotopy groups of this space are known to be finite. Given a compact Lie group $G$, this space can be regarded as an equivariant…

In this note we describe a family of arguments that link the homotopy-type of a) the diffeomorphism group of the disc $D^n$, b) the space of co-dimension one embedded spheres in a sphere and c) the homotopy-type of the space of co-dimension…

We construct a rational homotopy pullback decomposition for variants of the classifying space of the group of homeomorphisms for a large class of manifolds. This has various applications, including a rational section of the stabilisation…

Let $B$ be a M\"obius band and $f:B \to \mathbb{R}$ be a Morse map taking a constant value on $\partial B$, and $\mathcal{S}(f,\partial B)$ be the group of diffeomorphisms $h$ of $B$ fixed on $\partial B$ and preserving $f$ in the sense…

We show that the group ${\Cal D}(M)$ of pseudoisotopy classes of diffeomorphisms of a manifold of dimension $\geq 5$ and of finite fundamental group is commensurable to an arithmetic group. As a result $\pi_0(\text{{\it Diff\,M}})$ is a…

We prove explicit linear stable ranges for the $\mathsf{FI}$-modules $\mathrm{Hom}(\pi_p \mathrm{Conf} M, \mathbb Z)$ and $\mathrm{Ext}(\pi_p \mathrm{Conf} M, \mathbb Z)$ with $\mathrm{Conf} M$ being the configuration co$\mathsf{FI}$-space…

We prove that for many degrees in a stable range the homotopy groups of the moduli space of metrics of positive scalar curvature on S^n and on other manifolds are non-trivial. This is achieved by further developing and then applying a…

We will study homological stability of the diffeomorphism groups of the manifolds $W_{g,1}:=D^{2n} \# (S^n \times S^n)^{\#g }$ using $E_k$-algebras. This will lead to new improvements in the stability results, especially when working with…