arXiv research

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 homology of a subcritical Stein-filling of the contact manifold.

It is known by A. Loi and R. Piergallini that a closed, oriented, smooth 3-manifold is Stein fillable if and only if it has a positive open book decomposition. In the present paper we will show that for every link L in a Stein fillable 3-manifold there exists an additional knot L' to L such that the union of the links …

The topology of Stein surfaces and contact 3-manifolds is studied by means of handle decompositions. A simple characterization of homeomorphism types of Stein surfaces is obtained --- they correspond to open handlebodies with all handles of index lessthan or = 2. An uncountable collection of exotic R^4's is shown to ad…

Constructs knots with maximal Thurston-Bennequin number and creates reducible 3-manifolds.

New open books defy positive factorisation in genus one.

New method constructs Lefschetz fibrations with different regular fibers.

It is known that for coprime integers $p>q\geq 1$, the lens space $L(p^2,pq-1)$ bounds a rational ball, $B_{p,q}$, arising as the 2-fold branched cover of a (smooth) slice disk in $B^4$ bounding the associated 2-bridge knot. Lekilli and Maydanskiy give handle decompositions for each $B_{p,q}$. Whereas, Yamada gives an …

This paper classifies symplectic and Stein fillings of contact 3-manifolds with spinal open book decompositions.

In this article, using combinatorial techniques of mapping class groups, we show that a Stein fillable integral homology $3$-sphere supported by an open book decomposition with page a $4$-holed sphere admits a unique Stein filling up to diffeomorphism. Furthermore, according to a property of deforming symplectic fillin…

We prove that Stein surfaces with boundary coincide up to orientation preserving diffeomorphisms with simple branched coverings of $\B^4$ whose branch set is a positive braided surface. As a consequence, we have that a smooth oriented 3-manifold is Stein fillable iff it has a positive open-book decomposition.

The paper studies Stein-Weiss operators on symmetric tensors, extending previous work.

A simple method constructs Lefschetz fibrations on compact Stein surfaces.

An open subset U of a complex surface can be topologically perturbed to yield an open subset whose inherited complex structure is Stein, if and only if U is homeomorphic to the interior of a handlebody whose handles all have index equal or less than 2.

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 fillings as a sum of the signatures of basic relations in the monodromy of a related…

Elliptic surfaces without 1-handles proven for specific cases.

The study finds knots with Stein structures beyond the typical upper bound.

Handles decompositions reveal new open book structures.

The square root of Fredholm determinants causes numerical instabilities in option pricing models.

The paper defines a contact structure invariant from Heegaard Floer homology.

The paper describes handle decompositions and Kirby diagrams for plane algebraic curves.

We study the relationship between exotic R^4's and Stein surfaces as it applies to smoothing theory on more general open 4-manifolds. In particular, we construct the first known examples of large exotic R^4's that embed in Stein surfaces. This relies on an extension of Casson's Embedding Theorem for locating Casson han…

The study shows conditions for elliptic surfaces without 1-handles.

From any 4-dimensional oriented handlebody X without 3- and 4-handles and with b_2>0, we construct arbitrary many compact Stein 4-manifolds which are mutually homeomorphic but not diffeomorphic to each other, so that their topological invariants (their fundamental groups, homology groups, boundary homology groups, and …

A theorem on the existence of the unique minimal topologic handle decomposition of differentiable simply connected five-dimensional manifolds is proved. For a decomposition of this sort, the number of handles of each index is given.

We review Giroux's contact handles and contact handle attachments in dimension three and show that a bypass attachment consists of a pair of contact 1 and 2-handles. As an application we describe explicit contact handle decompositions of infinitely many pairwise non-isotopic overtwisted 3-spheres. We also give an alter…

Construct broken Lefschetz fibrations from handle decompositions.

Study handles in 4-manifolds with cyclic fundamental group.

The study describes handle decompositions and Kirby diagrams for line arrangements.

Study of contractible manifolds and their twists to determine if they are $S^4$.

Study compact PL 4-manifolds with special handle decompositions.

Harer-Kas-Kirby conjectured that every handle decomposition of the elliptic surface E(1)_{2,3} requires both 1- and 3-handles. We prove that the elliptic surface E(n)_{p,q} has a handle decomposition without 1-handles for $n\geq 1$ and (p,q)=(2,3),(2,5),(3,4),(4,5).

We show that every smooth closed oriented four-manifold admits a decomposition into two co- dimension zero submanifolds with common boundary. Each of these submanifolds carries a structure of a symplectic manifold with pseudo-convex boundary. This imply, in particular, that every smooth closed simply-connected four-man…

Study shows knots surgered elliptic surfaces admit handle decompositions without 1- and 3-handles.

A double pants decomposition of a 2-dimensional surface is a collection of two pants decomposition of this surface introduced in arXiv:1005.0073v2. There are two natural operations acting on double pants decompositions: flips and handle twists. It is shown in arXiv:1005.0073v2 that the groupoid generated by flips and h…

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 moves on such diagrams that do not change the corresponding contact manifold. As an …

On décrit ici des relations entre la géométrie globale des variétés de contact closes et celle de certaines variétés symplectiques, à savoir les variétés de Stein compactes. L'origine de ces relations est l'existence de livres ouverts adaptés aux structures de contact. We discuss relations between the global geometry o…

Skein lasagna module calculates 4-manifold invariants using handle decompositions.

Study rational homology balls using Casson-Gordon invariants to measure complexity.

Study on deformations of polynomials and their Milnor fibration topology.

Trisection method for 4-manifolds with boundary.

Improved SSD for faster and more accurate goodness-of-fit tests and model learning.

Estimates complex models without assuming Gaussian symmetry, achieving near-optimal performance.

New compression methods handle biased input sequences for more accurate posterior summaries.

The paper calculates a new invariant for 4-manifolds using handle decompositions and skein relations.

New insights into knot fusion numbers via cabling.

We determine the structure of the circular handle decompositions of the family of free genus one knots. Namely, if k is a free genus one knot, then the handle number h(k)= 0, 1 or 2, and, if k is not fibered (that is, if h(k)>0), then k is almost fibered. For this, we develop practical techniques to construct circular …

We study diffeomorphisms of compact, oriented surfaces, developing methods of distinguishing those which have positive factorizations into Dehn twists from those which satisfy the weaker condition of right veering. We use these to construct open book decompositions of Stein-fillable 3-manifolds whose monodromies have n…

New $4$-manifolds without $1$- and $3$-handles are created from knots.