Related papers: Corks with large shadow-complexity and exotic 4-ma…

Motivated by Stipsicz and Szab\'{o}'s exotic 4-manifolds with b_2^+=3 and b_2^-=8, we construct a family of simply connected smooth 4-manifolds with b_2^+=3 and b_2^-=8. As a corollary, we conclude that the topological 4-manifold…

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 an infinite family of contractible 4-manifolds have the same boundary as a special type of plumbing. Consequently their Ozsvath--Szabo invariants can be calculated algorithmically. We run this algorithm for the first few…

We give several criteria on a closed, oriented 3-manifold that will imply that it is the boundary of a (simply connected) 4-manifold that admits infinitely many distinct smooth structures. We also show that any weakly fillable contact…

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

We show that, under a certain condition, contact 5-manifolds can `coarsely' distinguish smooth structures on compact Stein 4-manifolds via contact open books. We also give a simple sufficient condition for an infinite family of Stein…

In $1961$, Mazur constructed a contractible, compact, smooth $4$-manifold with boundary which is not homeomorphic to the standard $4$-ball, using a $0$-handle, a $1$-handle and a $2$-handle. In this paper, for any integer $n\geq2,$ we…

We construct an infinite family of mutually non-diffeomorphic irreducible smooth structures on the topological 4-manifold $S^2 \times S^2$.

For 5 <= k <= 8 we show that the infinite family of exotic smooth structures on CP^2# k(-CP^2) can be achieved by 1/n - surgeries on a single embedded nullhomologous torus in a manifold R_k which is homeomorphic to CP^2# k(-CP^2).

We present a construction which shows that there is an infinite set of cyclically 4-edge connected cubic graphs on $n$ vertices with no cycle longer than $c_4 n$ for $c_4=\frac{12}{13}$, and at the same time prove that a certain natural…

We study the four infinite families KA(n), KB(n), KD(n), KQ(n) of finite dimensional Hopf (in fact Kac) algebras constructed respectively by A. Masuoka and L. Vainerman: isomorphisms, automorphism groups, self-duality, lattices of coideal…

For any integer $n\geq 2$, we construct an infinite family of Stein fillable contact $(4n-1)$-manifolds each of which admits infinitely many pairwise homotopy inequivalent Stein fillings.

We extend Masuoka's Theorem [11] concerning the isomorphism between the group of invertible bimodules in a non-commutative ring extension and the group of automorphisms of the associated Sweedler's canonical coring, to the class of finite…

We show that any finitely presented group with an index two subgroup is realized as the fundamental group of a closed smooth non-orientable four-manifold that admits an exotic smooth structure, which is obtained by performing a Gluck twist.…

In this short note, for each non-zero integer n, we construct a 4-manifold containing a smoothly concordant pair of spheres with a common dual of square n but no automorphism carrying one sphere to the other. Our examples, besides showing…

We construct an invariant of open four-manifolds using the Heegaard Floer theory of Ozsvath and Szabo. We show that there is a manifold X homeomorphic to R^4 for which the invariant is non-trivial, showing that X is an exotic R^4.

We show that any topological, closed, oriented, non-spin $4$-manifold with fundamental group $\mathbb{Z}_{4k}$ and $\min(b_2^+, b_2^-)\geq 15$, has either none or infinitely many distinct smooth structures. Furthermore, we construct…

We study extremality properties of covering families of rational curves on projective varieties. Among others, we show that on a normal and Q-factorial projective variety of dimension at most 4, every covering and quasi-unsplit family of…

Lickorish has constructed large families of contractible 4--manifolds that have knotted embeddings in the 4--sphere and has also shown that every finitely presented perfect group with balanced presentation occurs as the fundamental group of…

We introduce and study a class of compact 4-manifolds with boundary that we call protocorks. Any exotic pair of simply connected closed 4-manifolds is related by a protocork twist, moreover, any cork is supported by a protocork. We prove a…