arXiv research

Study describes prosoluble subgroups in 3-manifold groups.

We prove a finiteness result for the $\partial$-patterned guts decomposition of all 3-manifolds obtained by splitting a given orientable, irreducible and $\partial$-irreducible 3-manifold along a closed incompressible surface. Then using the Thurston norm, we deduce that the JSJ-pieces of all 3-manifolds dominated by a…

Compact flat surfaces of homogeneous Riemannian 3-manifolds with isometry group of dimension 4 are classified. Non-existence results for compact constant Gauss curvature surfaces in these 3-manifolds are established.

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

Paper proves Luo's conjecture for 3D triangulated manifolds.

We describe the compact Lorentzian $3$-manifolds admitting a parallel lightlike vector field. The classification of compact Lorentzian $3$-manifolds admitting non-isometric affine diffeomorphisms follows, together with the complete description of these morphisms. Such a Lorentzian manifold is in some sense an equivaria…

Matveev introduced Borromean surgery on 3-manifolds, and proved that the equivalence relation on closed, oriented 3-manifolds generated by Borromean surgeries is characterized by the first homology group and the torsion linking pairing. Massuyeau generalized this result to closed, spin 3-manifolds, and the second autho…

Classifies Nil 3-manifolds as cross-sections of complex hyperbolic surfaces.

Compactness theorem for 3-manifold Floer theory defined by Fueter sections.

Study on Cheeger constant in specific hyperbolic 3-manifolds.

The paper classifies quasi-Einstein 3-manifolds and their properties.

Extends fibering theorems for 3-manifolds.

New hyperbolic 3-manifolds have many neighbors.

Paper classifies transnormal systems on compact 3-manifolds.

Paper finds minimum volume for specific anti-de Sitter 3-manifolds.

Study shows diffeomorphism groups of certain 3-manifolds retract to isometry groups.

A triangulation of a compact 3-manifold is annular-efficient if it is 0-efficient and the only normal, incompressible annuli are thin edge-linking. If a compact 3-manifold has an annular-efficient triangulation, then it is irreducible, boundary-irreducible, and an-annular. Conversely, it is shown that for a compact, ir…

3-manifold groups can only have convex co-compact representations if they are geometric or hyperbolic.

We study the Birman exact sequence for compact 3-manifolds.

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

Proves unique hyperbolic metric for 3-manifolds with ideal triangulation.

Study shows infimum of dual volume equals convex core volume for hyperbolic 3-manifolds.

We study compact complex 3-manifolds admitting holomorphic Riemannian metrics. We prove a uniformization result: up to a finite unramified cover, such a manifold admits a holomorphic Riemannian metric of constant sectionnal curvature.

The study reveals a persistent bias in the distribution of holonomy on compact hyperbolic 3-manifolds.

Deciding 3-manifolds fibering over the circle is in NP

Study invariants of 3-manifold groups to determine Euler characteristics of 4-manifolds.

We show that the infinite cyclic cover of the exterior of the untwisted Whitehead double of a non-trivial knot does not embed in any compact 3-manifold, answering a question of Jiang, Ni, Wang and Zhou.

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…

We give a summary of known results on Matveev's complexity of compact 3-manifolds. The only relevant new result is the classification of all closed orientable irreducible 3-manifolds of complexity 10.

We introduce a representation of compact 3-manifolds without spherical boundary components via (regular) 4-colored graphs, which turns out to be very convenient for computer aided study and tabulation. Our construction is a direct generalization of the one given in the eighties by S. Lins for closed 3-manifolds, which …

Researchers found the minimum number of tetrahedra needed to triangulate elliptic and sol 3-manifolds.

The renormalized volume is reinterpreted using isoperimetric profiles.

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

We show that fundamental groups of compact, orientable, irreducible 3-manifolds with toroidal boundary are Grothendieck rigid.

In this paper it is proven that if the group of covering translations of the covering space of a compact, connected, $P^2$-irreducible 3-manifold corresponding to a non-trivial, finitely-generated subgroup of its fundamental group is infinite, then either the covering space is almost compact or the subgroup is infinite…

We prove that the deformation space $AH(M)$ of marked hyperbolic 3-manifolds homotopy equivalent to a fixed compact 3-manifold $M$ with incompressible boundary is locally connected at quasiconformally rigid points.

A universal branched 3-manifold $W$ characterizes Sol 3-manifolds.

We give definitions of cohomology determinants for compact, connected, orientable 3-manifolds. We also give formulae relating cohomology determinants before and after gluing a solid torus along a torus boundary component. Cohomology determinants are related to Turaev torsion, though the author hopes that they have othe…

We present a simple algorithm for finding eigenmodes of the Laplacian for arbitrary compact hyperbolic 3-manifolds. We apply our algorithm to a sample of twelve manifolds and generate a list of the lowest eigenvalues. We also display a selection of eigenmodes taken from the Weeks space.

Study homomorphisms from groups to 3-manifold fundamental groups.

Compactness theorem for 3D RS-SW equations on 3-manifolds.

We study the asymptotics of the number N(t) of geometrically distinct closed geodesics of a Riemannian or Finsler metric on a connected sum of two compact manifolds of dimension at least three with non-trivial fundamental groups and apply this result to the prime decomposition of a three-manifold. In particular we show…

New method finds infinitely many knots in 3-manifolds.

Finite type for 3-manifolds with boundary.

3-manifolds with positive scalar curvature have controlled foliations.

The idea of computing Matveev complexity by using Heegaard decompositions has been recently developed by two different approaches: the first one for closed 3-manifolds via crystallization theory, yielding the notion of Gem-Matveev complexity; the other one for compact orientable 3-manifolds via generalized Heegaard dia…

3-manifolds can be virtually dominated by maps of degree 8.

We enumerate the small-volume manifolds that can be obtained by Dehn filling on Mom-2 and Mom-3 manifolds as defined by Gabai, Meyerhoff, and the author. In so doing we complete the proof that the Weeks manifold is the minimum-volume compact hyperbolic 3-manifold, as well as enumerating the 10 smallest one-cusped hyper…