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For every $k geq 2$ and $n geq 2$ we construct $n$ pairwise homotopically inequivalent simply-connected, closed $4k$-dimensional manifolds, all of which are stably diffeomorphic to one another. Each of these manifolds has hyperbolic intersection form and is stably parallelisable. In dimension $4$, we exhibit an analogous phenomenon for spin$^{c}$ structures on $S^2 times S^2$. For $mgeq 1$, we also provide similar $(4m{-}1)$-connected $8m$-dimensional examples, where the number of homotopy types in a stable diffeomorphism class is related to the order of the image of the stable $J$-homomorphism $pi_{4m-1}(SO) to pi^s_{4m-1}$.
We study the set $widehat{mathcal S}_M$ of framed smoothly slice links which lie on the boundary of the complement of a 1-handlebody in a closed, simply connected, smooth 4-manifold $M$. We show that $widehat{mathcal S}_M$ is well-defined and describ
Let $G$ be a simply-connected simple compact Lie group and let $M$ be an orientable smooth closed 4-manifold. In this paper we calculate the homotopy type of the suspension of $M$ and the homotopy types of the gauge groups of principal $G$-bundles ov
We attach copies of the circle to points of a countable dense subset $D$ of a separable metric space $X$ and construct an earring space $E(X,D)$. We show that the fundamental group of $E(X,D)$ is isomorphic to a subgroup of the Hawaiian earring gro
We determine the number of distinct fibre homotopy types for the gauge groups of principal $Sp(2)$-bundles over a closed, simply-connected four-manifold.
We study several questions on the existence of negative Sasakian structures on simply connected rational homology spheres and on Smale-Barden manifolds of the form $#_k(S^2times S^3)$. First, we prove that any simply connected rational homology spher