Related papers: Small exotic Stein manifolds

The aim of this paper is to use mapping class group relations to approach the `geography' problem for Stein fillings of a contact 3-manifold. In particular, we adapt a formula of Endo and Nagami so as to calculate the signature of such…

In this paper we construct a family of simply connected, spin, non-complex, symplectic 4-manifolds which cover all but finitely many allowed lattice points $(\chi, c)$ lying in $0 \leq c \leq 8.76\chi$. Furthermore, as a corollary, we prove…

We exhibit infinitely many exotic pairs of simply-connected, closed $4$-manifolds not related by any cork of the infinite family $W_n$ constructed by Akbulut and Yasui whose first member is the Akbulut cork. In particular, the Akbulut cork…

While the exotic diffeomorphisms turned out to be very rich, we know much less about the $b^+_2 =2$ case, as parameterized gauge-theoretic invariants are not well defined. In this paper we present a method (that is, comparing the winding…

We show that, given a closed integral symplectic manifold $(\Sigma, \omega)$ of dimension $2n \geq 4$, for every integer $k>\int_{\Sigma}\omega^{n}$, the Boothby-Wang bundle over $(\Sigma, k\omega)$ carries no Stein fillable contact…

We extend a construction of Stipsicz-Szab\'{o} of infinitely many irreducible exotic smooth structures of some closed four-manifolds with even $b_2^+$ and fundamental group $\mathbb{Z}/2\mathbb{Z}$. We use the double node surgery and…

We show that there are contact 3-manifolds of support genus one which admit infinitely many Stein fillings, but do not admit arbitrarily large ones. These Stein fillings arise from genus-1 allowable Lefschetz fibrations with distinct…

In this paper, we show that the Ozsv\'ath-Szab\'o contact invariant $c^+(\xi)\in HF^+(-Y)$ of a contact 3-manifold $(Y,\xi)$ can be calculated combinatorially if $Y$ is the boundary of a certain type of plumbing $X$, and $\xi$ is induced by…

In this article, we prove a generalization of a theorem of Lisca-Matic to Stein cobordisms and develop a method for distinguishing certain Stein cobordisms using rotation numbers. Using these results along with standard techniques from…

In this paper the 5-dimensional contact SO(3)-manifolds are classified up to equivariant contactomorphisms. The construction of such manifolds with singular orbits requires the use of generalized Dehn twists. We show as an application that…

We show that for every sequence $(n_i)$, where each $n_i$ is either an integer greater than 1 or is $\infty$, there exists a simply connected open 3-manifold $M$ with a countable dense set of ends $\{e_i\}$ so that, for every $i$, the genus…

We show that any closed oriented 3-manifold can be topologically embedded in some simply-connected closed symplectic 4-manifold, and that it can be made a smooth embedding after one stabilization. As a corollary of the proof we show that…

Dimension 4 is the first dimension in which exotic smooth manifold pairs appear -- manifolds which are topologically the same but for which there is no smooth deformation of one into the other. Whilst smooth and triangulated 4-manifolds do…

We construct uncountably many simply connected open 3-manifolds with genus one ends homeomorphic to the Cantor set. Each constructed manifold has the property that any self homeomorphism of the manifold (which necessarily extends to a…

We provide sufficient conditions assuring that a suitably decorated 2-polyhedron can be thickened to a compact 4-dimensional Stein domain. We also study a class of flat polyhedra in 4-manifolds and find conditions assuring that they admit…

We use contact handle decompositions and a stabilization process to compute the cylindrical contact homology of a subcritical Stein-fillable contact manifold with vanishing first Chern class, and show that it is completely determined by the…

Many noncompact hyperbolic 3-manifolds are topologically complements of links in the 3-sphere. Generalizing to dimension 4, we construct a dozen examples of noncompact hyperbolic 4-manifolds, all of which are topologically complements of…

We show that there exists an exotic pair of $4$-manifolds with boundary whose trisection genera are $4$. We also construct genus-$3$ relative trisections for an infinite family of contractible $4$-manifolds introduced by Akbulut and Kirby.

According to Giroux, contact manifolds can be described as open books whose pages are Stein manifolds. For 5-dimensional contact manifolds the pages are Stein surfaces, which permit a description via Kirby diagrams. We introduce handle…

We use spinal open books to construct contact manifolds with infinitely many different Weinstein fillings in any odd dimension $> 1$, which were previously unknown for dimensions equal to $4n+1$. The argument does not involve understanding…