相关论文: Exotically knotted closed surfaces from Donaldson'…
This article is concerned with locally flatly immersed surfaces in simply-connected $4$-manifolds where the complement of the surface has fundamental group $\mathbb{Z}$. Once the genus and number of double points are fixed, we classify such…
We show that many explicit examples of exotic pairs of surfaces in a smooth 4-manifold become smoothly isotopic after one external stabilization with $S^2\times S^2$ or $CP^2\#\overline{CP^2}$. Our results cover surfaces produced by…
We study the possibility of realizing exotic smooth structures on punctured simply connected $4$-manifolds as leaves of a codimension one foliation on a compact manifold. In particular, we show the existence of uncountably many smooth open…
We show that $\mathbb{C}^2$ contains pairs of properly embedded, smooth complex curves that are isotopic through homeomorphisms but not diffeomorphisms of $\mathbb{C}^2$. The construction is based on realizing corks as branched covers of…
We construct a compact, contractible 4-manifold $C$, an infinite-order self-diffeomorphism $f$ of its boundary, and a smooth embedding of $C$ into a closed, simply connected 4-manifold $X$, such that the manifolds obtained by cutting $C$…
We discuss corks, and introduce new objects which we call plugs. Though plugs are fundamentally different objects, they also detect exotic smooth structures in 4-manifolds like corks. We discuss relation between corks, plugs and rational…
In this brief note, we show that there exist smooth 4-manifolds (with nonempty boundary) containing pairs of exotically knotted 2-spheres that remain exotic after one (either external or internal) stabilization. It follows that the ``one is…
One approach to produce a pair of homeomorphic-but-not-diffeomophic closed 4-manifolds is to find a knot which is smoothly slice in one but not the other. This approach has never been run successfully. We give the first examples of a pair…
The paper shows deep connections between exotic smoothings of small R^4, noncommutative algebras of foliations and quantization. At first, based on the close relation of foliations and noncommutative C*-algebras we show that cyclic…
Conjecturally, a knot is slice if and only if its positive Whitehead double is slice. We consider an analogue of this conjecture for slice disks in the four-ball: two slice disks of a knot are smoothly isotopic if and only if their positive…
A pair of closed, smooth $4$-manifolds $M$ and $M'$ are stably exotic if they are stably homeomorphic but not stably diffeomorphic, where stabilisation refers to connected sum with copies of $S^2 \times S^2$. Orientable stable exotica do…
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…
By using corks we construct diffeomorphic ribbon disks $D\subset B^{4}$, which are non-isotopic rel boundary to each other.
We obtain constraints on the topology of families of smooth $4$-manifolds arising from a finite dimensional approximation of the families Seiberg-Witten monopole map. Amongst other results these constraints include a families generalisation…
Every exotic pair in 4-dimension is obtained each other by twisting a {\it cork} or {\it plug} which are codimension 0 submanifolds embedded in the 4-manifolds. The twist was an involution on the boundary of the submanifold. We define cork…
We produce examples of pairwise non-diffeomorphic closed irreducible 4-manifolds with non-trivial free abelian fundamental group of rank less than three and small Euler characteristic. These exotic smooth structures become standard after…
In this paper, we investigate existence of inequivalent smooth structures on closed smooth non-orientable 4-manifolds building upon results of Akbulut, Cappell-Shaneson, Fintushel-Stern, Gompf, and Stolz. We add to the number of known…
Expanding on work by Conway, Orson, and Powell, we study the isotopy classes rel. boundary of nonorientable, compact, locally flatly embedded surfaces in $D^4$ with knot group $\mathbb{Z}_2$. In particular we show that if two such surfaces…
We relate the Donaldson invariants of two four-manifolds $X_i$ with embedded Riemann surfaces of genus 2 and self-intersection zero with the invariants of the manifold X which appears as a connected sum along the surfaces. When the original…
Building on the work of Nozaki, Sato and Taniguchi, we develop an instanton-theoretic invariant aimed at studying strong corks and equivariant bounding. Our construction utilizes the Chern-Simons filtration and is qualitatively different…