Related papers: Cork twisting exotic Stein 4-manifolds

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…

In this article, we construct countably many mutually non-isotopic diffeomorphisms of some closed non simply-connected 4-manifolds that are homotopic to but not isotopic to the identity, by surgery along $\Theta$-graphs. As corollaries of…

We prove necessary and sufficient conditions for the existence of non-trivial Steenrod actions on the mod-$2$ cohomology of 4-dimensional toric orbifolds. As applications, the stable homotopy type and the gauge groups of a $4$-dimensional…

We describe a necessary and sufficient condition for a principal circle bundle over an even-dimensional manifold to carry an invariant contact structure. As a corollary it is shown that all circle bundles over a given base manifold carry an…

We describe a collection of constructions which illustrate a panoply of ``exotic'' smooth 4-manifolds.

We construct using Lefschetz fibrations a large family of contact manifolds with the following properties: Any bounding contact embedding into an exact symplectic manifold satisfying a mild topological assumption is non-displaceable and…

We construct infinitely many pairwise non-diffeomorphic smooth structures on a definite $4$-manifold with non-cyclic fundamental group $\mathbb{Z}/2\times \mathbb{Z}/2$.

We use a variation of a classical construction of A. Hatcher to construct virtually all stable exotic smooth structures on compact smooth manifold bundles whose fibers have sufficiently large odd dimension (at least twice the base dimension…

Let $M$ be $\CP#2\CPb$, $3\CP#4\CPb$ or $(2n-1)\CP#2n\CPb$ for any integer $n\geq 3$. We construct an irreducible symplectic 4-manifold homeomorphic to $M$ and also an infinite family of pairwise non-diffeomorphic irreducible non-symplectic…

Building on the algebraic framework developed by Hendricks, Manolescu, and Zemke, we introduce and study a set of Floer-theoretic invariants aimed at detecting corks. Our invariants obstruct the extension of a given involution over any…

We generalise the Kreck-Stolz invariants s_2 and s_3 by defining a new invariant, the t-invariant, for quaternionic line bundles E over closed spin-manifolds M of dimension 4k-1 with H^3(M; \Q) = 0 such that c_2(E)\in H^4(M) is torsion. The…

We produce infinite families of exotic actions of finite cyclic groups on simply connected smooth 4-manifolds with nontrivial Seiberg-Witten invariants.

A trisection of a smooth, closed, oriented 4-manifold is a decomposition into three 4-dimensional 1-handlebodies meeting pairwise in 3-dimensional 1-handlebodies, with triple intersection a closed surface. The fundamental groups of the…

For any finitely presentable group $G$, we show the existence of an isolated complex surface singularity link which admits infinitely many exotic Stein fillings such that the fundamental group of each filling is isomorphic to $G$. We also…

We show that there exist infinitely many pairwise distinct non-closed G_2-manifolds (some of which have holonomy full G_2) such that they admit co-oriented contact structures and have co-oriented contact submanifolds which are also…

Loi and Piergallini showed that a smooth compact, connected $4$-manifold $X$ with boundary admits a Stein structure if and only if $X$ is a simple branched cover of a $4$-disk $D^4$ branched along a positive braided surface $S$ in a bidisk…

This paper is the second part of our work on 4-dimensional 2-handlebodies. In the first part (arXiv:math.GT/0407032) it is shown that up to certain set of local moves, connected simple coverings of B^4 branched over ribbon surfaces,…

We construct and study the skein lasagna module obtained by importing the Bar-Natan Khovanov homology package. For 4-manifolds satisfying a non-vanishing condition, we produce pairs of exotic surfaces (with boundary) by using the behavior…

We describe a construction procedure of infinite sets of $2$-links in closed simply connected 4-manifolds that are topologically isotopic, smoothly inequivalent and componentwise topologically unknotted. These 2-links are the first examples…

Inspired by a recent result of Levine-Lidman-Piccirillo, we construct infinitely many exotic smooth structures on some closed four-manifolds with definite intersection form and fundamental group isomorphic to $\Z /2\Z$. Similar…