Related papers: Stein 4-manifolds and corks

For suitable finite groups G, we construct contractible 4-manifolds C with an effective G-action on $\partial C$ whose associated pairs (C,g) for all $g \in G$ are distinct smoothings of the pair $(C,\partial C)$. Indeed C embeds in a…

We provide an approach to study exotic phenomena in relatively small 4-manifolds that captures many different exotic behaviors under one umbrella. These phenomena include exotic smooth structures on 4-manifolds with $b_2=1$, examples of…

For any positive integer $n$ we give a ${\mathbb Z}^n$-cork with a ${\mathbb Z}^n$-effective embedding in a 4-manifold being homeomorphic to $E(n)$. This means that a cork gives a subset ${\mathbb Z}^n$ in the differential structures on…

It is known that the only Stein filling of the standard contact structure on S^3 is B^4. In this paper, we construct simply connected exotic compact Stein 4-manifold pairs for any Betti number $b_2 \geq 1$; we do this by enlarging corks and…

The author recently proved the existence of an infinite order cork: a compact, contractible submanifold $C$ of a 4-manifold and an infinite order diffeomorphism $f$ of $\partial C$ such that cutting out $C$ and regluing it by distinct…

We prove that every 4-dimensional oriented handlebody without 3- and 4-handles can be modified to admit infinitely many exotic smooth structures, and moreover prove that their genus functions are pairwise equivalent. We furthermore show…

We provide the first information on diffeotopy groups of exotic smoothings of R^4: For each of uncountably many smoothings, there are uncountably many isotopy classes of self-diffeomorphisms. We realize these by various explicit group…

For a 4-manifold represented by a framed knot in $S^3$, it has been well known that the 4-manifold admits a Stein structure if the framing is less than the maximal Thurston-Bennequin number of the knot. In this paper, we prove either the…

We show that every smooth closed oriented four-manifold admits a decomposition into two co- dimension zero submanifolds with common boundary. Each of these submanifolds carries a structure of a symplectic manifold with pseudo-convex…

We introduce a method to detect exotic surfaces without explicitly using a smooth 4-manifold invariant or an invariant of a 4-manifold-surface pair in the construction. Our main tools are two versions of families (Seiberg-Witten)…

The purpose of this article is twofold. First we outline a general construction scheme for producing simply-connected minimal symplectic 4-manifolds with small Euler characteristics. Using this scheme, we illustrate how to obtain…

A simple characterization is given of open subsets of a complex surface that smoothly perturb to Stein open subsets. As applications, complex 2-space C^2 contains domains of holomorphy (Stein open subsets) that are exotic R^4's, and others…

We prove a localization theorem for exotic diffeomorphisms, showing that every diffeomorphism of a compact simply-connected 4-manifold that is isotopic to the identity after stabilizing with one copy of $S^2 \times S^2$, is smoothly…

We construct an infinite family $\{ C_{n,k}\}_{k=1}^{\infty}$ of corks of Mazur type satisfying $2n\leq \mathrm{sc}^{\mathrm{sp}}(C_{n,k})\leq O(n^{3/2})$ for any positive integer $n$. Furthermore, using these corks, we construct an…

We study the relationship between exotic R^4's and Stein surfaces as it applies to smoothing theory on more general open 4-manifolds. In particular, we construct the first known examples of large exotic R^4's that embed in Stein surfaces.…

It is well known that for any exotic pair of simply connected closed oriented 4-manifolds, one is obtained from the other by twisting a compact contractible submanifold via an involution on the boundary. By contrast, here we show that for…

We show that for any po sitive integer $m$, there exist order $n$ Stein corks. The boundaries are cyclic branched covers of slice knots embedded in the boundary of corks. By applying these corks to generalized forms, we give a method…

This paper studies properly embedded surfaces in the 4-ball that are exotically knotted (i.e., topologically but not smoothly isotopic), and leverages this local phenomenon to study surfaces in larger 4-manifolds. The main results provide a…

In this article, we construct infinitley many simply connected, nonsymplectic and pairwise nondiffeomorphic 4-manifolds starting from E(n) and applying the sequence of knot surgery, ordinary blowups and rational blowdown. We also compute…

By using corks we construct diffeomorphic ribbon disks $D\subset B^{4}$, which are non-isotopic rel boundary to each other.