Related papers: Exotic diffeomorphisms on $4$-manifolds with $b_2^…
We show that there exist infinitely many simply connected compact Stein 4-manifolds with b_2=2 such that they are all homeomorhic but mutually non-diffeomorphic, and they are Stein fillings of the same contact 3-manifold on their…
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…
This paper is a step towards the complete topological classification of {\Omega}-stable diffeomorphisms on an orientable closed surface, aiming to give necessary and sufficient conditions for two such diffeomorphisms to be topologically…
The broken genera are orientation preserving diffeomorphism invariants of closed oriented 4-manifolds, defined via broken Lefschetz fibrations. We study the properties of the broken genera invariants, and calculate them for various…
In the framework of the PDE's algebraic topology, previously introduced by A. Pr\'astaro, are considered {\em exotic differential equations}, i.e., differential equations admitting Cauchy manifolds $N$ identifiable with exotic spheres, or…
We present new computational methods for proving diffeomorphy of triangulated 4-manifolds, including algorithms and topological software that can for the first time effectively handle the complexities that arise in dimension four and be…
It is well known that, among closed spherical Seifert three-manifolds, only lens spaces and prism manifolds admit several Seifert fibrations which are not equivalent up to diffeomorphism. Moreover the former admit infinitely many…
We describe the topological structure of closed manifolds of dimension no less than four which admit Morse-Smale diffeomorphisms such that its non-wandering set contains any number of sink periodic points, and any number of source periodic…
We introduce a variant of contact homology for convex open contact manifolds. As an application, we prove the existence of (in fact, infinitely many) exotic tight contact structures on $\mathbb{R}^{2n-1}$ for all $n>2$.
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 describe interrelations between a topology structure of closed manifolds (orientable and non-orientable) of the dimension $n\geq 4$ and the structure of the non-wandering set of regular homeomorphisms, in particular, Morse-Smale…
A short survey of exotic smooth structutes on 4-manifolds is given with a special emphasis on the corresponding cork structures. Along the way we discuss some of the more recent results in this direction, obtained jointly with R.Matveyev,…
Any smooth, closed oriented 4-manifold has a surface diagram of arbitrarily high genus g>2 that specifies it up to diffeomorphism. The goal of this paper is to prove the following statement: For any smooth, closed oriented 4-manifold M,…
Closed (and simply-connected) manifolds whose dimensions are greater than 4 are classified via sophisticated algebraic and abstract theory such as surgery theory and homotopy theory. It is difficult to handle 3 or 4-dimensional closed…
We proved that the boundary Dehn twist on the Milnor fiber $M_c(2, q, r)$ is an exotic diffeomorphism relative to the boundary if $q, r$ are odd, coprime integers bigger than $3$ and $(q-1)(r-1)/4$ is an odd number. The proof is given by…
We construct the first exotic $\mathbb C \mathbb P^2 \# 4 \overline{\mathbb C \mathbb P^2}$ by means of rational blowdowns. Similarly, we construct the first exotic $3\mathbb C \mathbb P^2 \# b^- \overline{\mathbb C \mathbb P^2}$ for…
We relate degree one grasper families of embedded circles to various constructions of diffeomorphisms found in the literature -- theta clasper classes of Watanabe, barbell diffeomorphisms of Budney and Gabai, and twin twists of Gay and…
The aim of the present paper is to study conditions under which all the non-wandering points are periodic points, for a discrete dynamical system of two variables defined on a compact manifold. We include a survey of known results in all…
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…
In this paper, we first prove that any closed simply connected 4-manifold that admits a decomposition into two disk bundles of rank greater than 1 is diffeomorphic to one of the standard elliptic 4-manifolds: $\mathbb{S}^4$,…