arXiv research

New symplectic operations replace certain 4-manifolds with simpler ones.

Let $Σ$ be a surface of negative Euler characteristic together with a pants decomposition $¶$. Kra's plumbing construction endows $Σ$ with a projective structure as follows. Replace each pair of pants by a triply punctured sphere and glue, or `plumb', adjacent pants by gluing punctured disk neighbourhoods of the punctu…

We define the basket number, the flat plumbing number and the flat plumbing basket number of a link. Then we provide some upperbounds for these plumbing numbers by using Seifert's algorithm. We study the relation between these plumbing numbers and the genera of links.

Flat plumbing basket surfaces of links were introduced to study the geometry of the complement of the links. These flat plumbing basket surface can be presented by a sequential presentation known as flat plumbing basket code first found by Furihata, Hirasawa and Kobayashi. The minimum number of flat plumbings to obtain…

Study connects plumbing baskets to 3-sphere contact structures.

The existence of basket, flat plumbing and flat plumbing basket surfaces of a link was first proven from a braid representative of the link. In the present article, we show the existence of such surfaces from an induced graph of the link. Consequently, we define the basket number, flat plumbing number and flat plumbing…

Flat plumbing basket surfaces of links were introduced to study the geometry of the complement of the links. In present article, we study links of the flat plumbing basket numbers $4$ or less using a special presentation of the flat plumbing basket surfaces. We find a complete classification theorem of links of the fla…

The paper constructs a Legendrian link from a flat plumbing basket and relates its properties to the self-linking and Thurston-Bennequin numbers.

We define and prove properties of link lattice complexes for plumbed links.

New $\hat{Z}$ invariant for plumbed 3-manifolds with detailed computations and conjectures.

New quantum modular forms for specific 3-manifolds discovered.

Algorithm transforms weakly negative plumbing trees to negative definite ones.

Proves a plumbing-multiplicative property of a Links-Gould invariant.

Study homology cobordism and plumbed manifolds using Heegaard Floer homology.

We consider double plumbings of two disk bundles over spheres. We calculate the Heegaard-Floer homology with its absolute grading of the boundary of such a plumbing. Given a closed smooth 4-manifold $X$ and a suitable pair of classes in $H_{2}(X)$, we investigate when this pair of classes may be represented by a config…

We give a criterion for an open book to contain an n-times iterated Hopf plumbing summand. As an application, we show that fibre surfaces of positive braid knots admit a trefoil plumbing structure.

Plumbing of surfaces embeds in hyperbolic 4-manifolds.

New invariant connects knot homology and BPS series for plumbed knot complements.

Fintushel and Stern defined the rational blow-down construction [FS] for smooth 4-manifolds, where a linear plumbing configuration of spheres $C_n$ is replaced with a rational homology ball $B_n$, $n \geq 2$. Subsequently, Symington [Sy] defined this procedure in the symplectic category, where a symplectic $C_n$ (given…

Study series invariants of plumbed 3-manifolds using root lattices.

New method for calculating crosscap numbers of knots.

New invariants measure how far spanning surfaces are from being compressible.

Four constructions of Seifert surfaces - Hopf plumbing, arborescent plumbing, basketry, and T-bandword handle decomposition - are described, and some interrelationships found, e.g.: arborescent Seifert surfaces are baskets; Hopf-plumbed baskets are precisely homogeneous T-bandword surfaces. A Seifert surface is Hopf-pl…

Study tight contact structures on specific 3-manifolds.

This paper classifies minimal fillings of lens spaces.

Study on $Δ$ invariants of plumbed 3-manifolds, comparing with Heegaard-Floer homology.

Study properties of contact structures on symplectic disk bundles with concave boundaries.

Let M be a rational homology sphere plumbed 3-manifold associated with a connected negative definite plumbing graph. We show that its Seiberg-Witten invariants equal certain coefficients of an equivariant multivariable Ehrhart polynomial. For this, we construct the corresponding polytopes from the plumbing graphs toget…

Algorithm calculates polynomial Seiberg-Witten invariant from zeta-function of plumbed 3-manifolds.

Study series invariants for plumbed 3-manifolds and their properties.

Study Heegaard Floer homology of plumbed 3-manifolds, proving infinite-rank subgroup existence.

The paper classifies tight contact structures on specific plumbed 3-manifolds.

Proves conjecture linking WRT invariants and homological blocks for plumbed 3-manifolds.

Let $L$ be an oriented link with an alternating diagram $D$. It is known that $L$ is a fibered link if and only if the surface $R$ obtained by applying Seifert's algorithm to $D$ is a Hopf plumbing. Here, we call $R$ a Hopf plumbing if $R$ is obtained by successively plumbing finite number of Hopf bands to a disk. In t…

New indefinite false theta functions match homological blocks for a specific 3-manifold.

Instanton Floer homology matches Heegaard Floer for almost-rational plumbings.

Computes Pin(2)-equivariant monopole Floer homology for certain plumbed 3-manifolds.

Classifies 5D stationary black hole domains using plumbing and disc bundles.

Khovanov homology is simplified for plumbing operations.

A closer look at an example introduced by Livingston & Melvin and later studied by Miyazaki shows that a plumbing of two fibered ribbon knots (along their fiber surfaces) may be algebraically slice yet not ribbon.

We construct smooth 4-manifolds homeomorphic but not diffeomorphic to $CP^2#k\bar{CP^2},k \in {6,7,8,9}$, using the technique of rational blow-down along Wahl type plumbing trees of spheres.

Study lens spaces' definite fillings, classifying those with specific inequalities.

Researchers create non-normal affine structures for 3-manifolds, calculating Poincaré series.

In this paper, we introduce a category of graded commutative rings with certain algebraic morphisms, to investigate the cobordism category of plumbed 3-manifolds. In particular, we define a non-associative distributive algebra that gives necessary conditions for an abstract morphism between the homologies of two plumbe…

Homogeneous braids are visually prime, solving a Cromwell question.

C-gluing constructs quasi-Fuchsian structures on surfaces.

New method determines arrangement combinatorics from Milnor fiber boundary.

We describe explicit open books on arbitrary plumbings of oriented circle bundles over closed oriented surfaces. We show that, for a non-positive plumbing, the open book we construct is horizontal and the corresponding compatible contact structure is also horizontal and Stein fillable. In particular, we describe horizo…