arXiv research

Paper shows unique decomposition of 3-manifolds and multiplicative property of Reidemeister torsion.

The paper defines and proves stabilization for 3-manifold decompositions with multibranched surface intersections.

Study the JSJ-decomposition of a specific 3-manifold.

The study provides a structure theorem for a new class of noncompact 3-manifolds.

New 3D shapes can't be split into torus pieces.

Study handles in 3D shapes, applies to material patterns.

The profinite completion of the fundamental group of a closed, orientable $3$-manifold determines the Kneser--Milnor decomposition. If $M$ is irreducible, then the profinite completion determines the Jaco--Shalen--Johannson decomposition of $M$.

Classifies Morse boundaries of 3-manifold groups.

A pants-block decomposition of a 3-manifold is similar to a triangulation of a 3-manifold in many aspects. In this paper we show that any two pants-block decompositions of a 3-manifold are related by a finite sequence of moves which are called P-moves. The P-moves between pants-block decompositions are similar to the P…

Study of 3-manifolds in 5-sphere using bridge decompositions.

Finite Goeritz groups for links with long bridge decompositions.

3-manifolds with toral boundary are uniquely determined by their profinite completions.

Proves hyperbolic 3-manifolds have angle structures under certain conditions.

We describe a new approach to the canonical decompositions of 3-manifolds along tori and annuli due to Jaco-Shalen and Johannson (with ideas from Waldhausen) - the so-called JSJ-decomposition theorem. This approach gives an accessible proof of the decomposition theorem; in particular it does not use the annulus-torus t…

Researchers compute Goeritz groups for all (1,1)-link decompositions.

We use convex decomposition theory to (1) reprove the existence of a universally tight contact structure on every irreducible 3-manifold with nonempty boundary, and (2) prove that every toroidal 3-manifold carries infinitely many nonisotopic, nonisomorphic tight contact structures.

The paper detects fiberedness in 3-manifolds and extends a torsion invariant to sutured manifolds.

Invariants for 3-manifolds with toral boundaries, related by sutured decompositions.

It has been shown by V. Colin that every tight contact 3-manifold can be written as a connected sum of prime manifolds. Here we prove that the summands in this decomposition are unique up to order and contactomorphism.

We show that open 3-manifolds that have a locally finite decomposition along 2-spheres are characterized by the existence of a Riemannian metric with respect to which the second homotopy group of the manifold is generated by small elements.

Study of Ricci-Yamabe solitons on Walker 3-manifolds.

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 …

Motivated by the algorithmic study of 3-dimensional manifolds, we explore the structural relationship between the JSJ decomposition of a given 3-manifold and its triangulations. Building on work of Bachman, Derby-Talbot and Sedgwick, we show that a "sufficiently complicated" JSJ decomposition of a 3-manifold enforces a…

Surveying recent progress on hyperbolic 3-manifold rigidity.

In this paper we extend previous results concerning the behaviour of JSJ decompositions of closed 3-manifolds with respect to the profinite completion to the case of compact 3-manifolds with boundary. We also illustrate an alternative and perhaps more natural approach to part of the original theorem, using relative coh…

3D contact forms have supporting decompositions, leading to entropy results.

We prove a decomposition formula for twisted Blanchfield pairings of 3-manifolds. As an application we show that the twisted Blanchfield pairing of a 3-manifold obtained from a 3-manifold Y with a representation $φ: Z[π_1(Y)] \to R$, infected by a knot J along a curve $η$ with $φ(η) \neq 1$, splits orthogonally as the …

The paper finds lower bounds on hyperbolic 3-manifold volumes.

We establish an existence and uniqueness theorem for prime decompositions of theta-curves in $3$-manifolds.

New proof of Giroux Correspondence for tight contact 3-manifolds.

In this paper, we give a complete characterization on which finitely generated subgroups of finitely generated $3$-manifold groups are separable. Our characterization generalizes Liu's spirality character on $π_1$-injective immersed surface subgroups of closed $3$-manifold groups. A consequence of our characterization …

The paper classifies decompositions of 3-sphere and lens spaces with handlebodies.

This paper uses combinatorial Ricci flow to tackle Thurston's triangulation conjecture.

New theorem allows transverse links to be braided with rational book structure.

A real 3-manifold is a smooth 3-manifold together with an orientation preserving smooth involution, called a real structure. In this article we study open book decompositions on smooth real 3-manifolds that are compatible with the real structure. We call them real open book decompositions. We show that each real open b…

We provide a complete set of two moves that suffice to relate any two open book decompositions of a given 3-manifold. One of the moves is the usual plumbing with a positive or negative Hopf band, while the other one is a special local version of Harer's twisting, which is presented in two different (but stably equivale…

Simplified proof classifies surfaces using normal curves.

We compute the Minimal Entropy of every closed, orientable $3$-manifold, showing that its cube equals the sum of the cubes of the minimal entropies of each hyperbolic component arising from the $JSJ$ decomposition of each prime summand. As a consequence we show that the cube of the Minimal Entropy is additive with resp…

The abstract discusses applications of Menke's JSJ decomposition to symplectic fillings of various 3-manifolds.

The chromatic number of sphere graphs in 3-manifolds is bounded.

We give a sufficient condition for an open 3-manifold to admit a decomposition along properly embedded open annuli and tori, generalizing the toric splitting of Jaco-Shalen and Johannson.

We give examples of open 3-manifolds and 3-orbifolds that exhibit pathological behavior with respect to splitting along surfaces (2-suborbifolds) with nonnegative Euler characteristic.

Study the moduli space of reducible 3-manifolds using prime decomposition.

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

Scharlemann and Thompson define a numerical complexity for a 3-manifold using handle decompositions of the manifold. We show that for compact hyperbolic 3-manifolds this is linearly related to a definition of metric complexity in terms of the areas of level sets of Morse functions.

3-manifold groups have a property that allows them to act on quasi-trees.

New technique connects instanton Floer homology to Heegaard diagrams for knots and 3-manifolds.

This paper describes a characterization of tightness of closed contact 3-manifolds in terms of supporting open book decompositions. The main result is that tightness of a closed contact 3-manifold is preserved under Legendrian surgery.