Related papers: An exotic smooth structure on CP^2+6CP^2-bar

We study a family of birational maps of smooth affine quadric 3-folds, {over the complex numbers}, of the form $x_1x_4-x_2x_3=$ constant, which seems to have some (among many others) interesting/unexpected characters: a) they are…

A complex projective tower or simply a $\mathbb CP$-tower is an iterated complex projective fibrations starting from a point. In this paper we classify all 6-dimensional $\mathbb CP$-towers up to diffeomorphism, and as a consequence, we…

We consider simply-connected $4$-manifolds admitting Lefschetz fibrations over the $2$-sphere. We explicitly construct nonhyperelliptic and hyperelliptic Lefschetz fibrations of genus $4$ on simply-connected $4$-manifolds which are exotic…

For a symplectic manifold $(M,\om)$ with exact symplectic form we construct a 2-cocycle on the group of symplectomorphisms and indicate cases when this cocycle is not trivial.

We prove that any closed simply-connected smooth 4-manifold is 16-fold branched covered by a product of an orientable surface with the 2-torus, where the construction is natural with respect to spin structures. In particular this solves…

We provide information on diffeotopy groups of exotic smoothings of punctured 4-manifolds, extending previous results on diffeotopy groups of exotic $\mathbb{R}^4$'s. In particular, we prove that for a smoothable 4-manifold $M$ and for a…

This paper explores various differentiable structures on the product manifold $M \times \mathbb{S}^k$, where $M$ is either a 4-dimensional closed, oriented, smooth manifold or a simply connected 5-dimensional closed, smooth manifold. We…

In this paper, given a knot K, for any integer m we construct a new surface Sigma_K(m) from a smoothly embedded surface Sigma in a smooth 4-manifold X by performing a surgery on Sigma. This surgery is based on a modification of the `rim…

In this paper the singular hypersurfaces in $\mathbb{C}\mathrm{P}^4$ of degree $d$ with an isolated singularity are studied. If the singularity is of type $A_{2k+1}$, under the condition $d<(k+5)/2$, a classification of such hypersurfaces…

We analyze the symplectic and complex structures on the panelled web 4-manifolds. In particular, we give infinite family of examples of almost complex but not symplectic and not complex 4-manifolds in the non-simply connected case.

Cappell-Shaneson homotopy 4-spheres (CS spheres) are potential counterexamples of the smooth 4-dimensional Poincar\'e conjecture. Akbulut proved that infinite CS spheres are diffeomorphic to the standard 4-sphere by Kirby calculus. Kim and…

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.

The main result is that an s-cobordism (topological or smooth) of 4-manifolds has a product structure outside a ``core'' sub s-cobordism. These cores are arranged to have quite a bit of structure, for example they are smooth and abstractly…

We present a method for finding embedded nullhomologous tori in standard 4-manifolds which can be utilized to change their smooth structure. As an application, we show how to obtain infinite families of simply connected smooth 4-manifolds…

We show that any simply connected topological closed $4$-manifold punctured along any compact, totally disconnected tame subset $\Lambda$ admits a continuum of smoothings which are not diffeomorphic to any leaf of a $C^{1,0}$ codimension…

In this paper, we study stable equivalence of exotically knotted surfaces in 4-manifolds, surfaces that are topologically isotopic but not smoothly isotopic. We prove that any pair of embedded surfaces in the same homology class become…

We construct a smooth hyperbolic volume preserving diffeomorphism on a four dimensional compact Riemannian manifold which has countably many ergodic components and is arbitrarily close to the identity map.

This note provides a variational description of the most basic differential geometric structures on a smooth manifold.

Manolescu and Piccirillo recently initiated a program to construct an exotic $S^4$ or $\# n \mathbb{CP}^2$ by using zero surgery homeomorphisms and Rasmussen's $s$-invariant. They find five knots that if any were slice, one could construct…

A metric with positive sectional curvature on the Gromoll-Meyer exotic 7-sphere is constructed explicitly. The proof relies on a 2-parameter family of left invariant metrics on Sp(2) and a one-parameter family of conformal deformations via…