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For every $k geq 2$ we construct infinitely many $4k$-dimensional manifolds that are all stably diffeomorphic but pairwise not homotopy equivalent. Each of these manifolds has hyperbolic intersection form and is stably parallelisable. In fact we construct infinitely many such infinite sets. To achieve this we prove a realisation result for appropriate subsets of Krecks modified surgery monoid $ell_{2q+1}(mathbb{Z}[pi])$, analogous to Walls realisation of the odd-dimensional surgery obstruction $L$-group $L_{2q+1}^s(mathbb{Z}[pi])$.
Surgery triangles are an important computational tool in Floer homology. Given a connected oriented surface $Sigma$, we consider the abelian group $K(Sigma)$ generated by bordered 3-manifolds with boundary $Sigma$, modulo the relation that the three
It is shown that any closed three-manifold M obtained by integral surgery on a knot in the three-sphere can always be constructed from integral surgeries on a 3-component link L with each component being an unknot in the three-sphere. It is also inte
We define the stabilizing number $operatorname{sn}(K)$ of a knot $K subset S^3$ as the minimal number $n$ of $S^2 times S^2$ connected summands required for $K$ to bound a nullhomotopic locally flat disc in $D^4 # n S^2 times S^2$. This quantity is d
Suppose that $n eq p^k$ and $n eq 2p^k$ for all $k$ and all primes $p$. We prove that for any Hausdorff compactum $X$ with a free action of the symmetric group $mathfrak S_n$ there exists an $mathfrak S_n$-equivariant map $X to {mathbb R}^n$ whose im
Surgery exact triangles in various 3-manifold Floer homology theories provide an important tool in studying and computing the relevant Floer homology groups. These exact triangles relate the invariants of 3-manifolds, obtained by three different Dehn