arXiv research

New method to calculate 3-manifold invariants via skew-racks.

Survey on L^2-invariants for 3-manifolds.

New relation found between 3-manifold Witt invariants and $\hat{Z}$-invariants.

Study $Θ$-invariants for spherical 3-manifolds via $\mathbb{Z}π$-homology equivalences.

New invariants derived from a modular category for links and 3-manifolds.

Power series invariant of hyperbolic 3-manifolds matches knot invariants.

New invariants for 3-manifolds using special G-systems.

New invariant unifies two theories of 3-manifolds, recovering quantum invariants.

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

New gauge invariants from framed 3-manifolds match Hopf algebra indicators.

Study Turaev-Viro invariants of Seifert fibered 3-manifolds, proving volume conjecture.

New invariant from quantum algebra for 3-manifold bundles.

Study Turaev-Viro invariants of 3-manifolds with toroidal boundary.

Equivalent categories of groups and risandles for 3-manifolds.

Computes Vafa-Witten invariants of 3-manifolds.

The Kuperberg invariant is shown to be gauge invariant for certain framed 3-manifolds.

The abstract discusses conjectures about Chern-Simons invariants of 3-manifolds.

A new quantum gauge model is proposed. From this quantum gauge model we derive a quantum invariant of 3-manifolds. We show that this quantum invariant of 3-manifolds gives a classification of closed (orientable and connected) 3-manifolds. From this classification we then prove the Poincaré conjecture.

Quantum invariants of 3-manifolds and links reviewed, with connections to other topological invariants.

We introduce a generalization of the Dijkgraaf-Witten invariants for cusped or compact oriented 3-manifolds. We show that the generalized DW invariants distinguish some pairs of cusped hyperbolic 3-manifolds with the same hyperbolic volumes and with the same Turaev-Viro invariants. We also present an example of a pair …

Neumann's work connects 3-manifold invariants to quantum topology.

New quantum invariant for framed 3-manifolds using ideal triangulations.

Extends Milnor's invariants to 3-manifolds, solving an open problem.

New invariants derived from Kauffman bracket for 3-manifolds.

Researchers prove quantum invariants remain hard even when restricted.

Invariants of 3-manifolds using modified Hopf G-coalgebra.

Formula calculates invariant for 3-manifolds with torus boundaries.

We construct a simple topological invariant of certain 3-manifolds, including quotients of the 3-sphere by finite groups, based on the fact that the tangent bundle of an orientable 3-manifold is trivialisable. This invariant is strong enough to yield the classification of lens spaces of odd, prime order. We also use pr…

Motivated by the Turaev-Viro invariant of 3-manifolds, we construct a formal topological invariant of closed, oriented 3-manifolds involving spherical tetrahedra as an application of the asymptotic formula of 6j symbols for the Quantum Enveloping Algebra of sl(2). This invariant can be considered as a spherical version…

New invariant for spin 3-manifolds using super 3-cocycles.

In this paper, it is explained that a topological invariant for 3-manifold $M$ with $b_1(M)=1$ can be constructed by applying Fukaya's Morse homotopy theoretic approach for Chern--Simons perturbation theory to a local system on $M$ of rational functions associated to the free abelian covering of $M$. Our invariant take…

Enhanced bounds on rho-invariants for 3-manifolds.

Bordered Floer homology assigns invariants to 3-manifolds with boundary, such that the Heegaard Floer homology of a closed 3-manifold, split into two pieces, can be recovered as a tensor product of the bordered invariants of the pieces. We construct cornered Floer homology invariants of 3-manifolds with codimension-2 c…

New invariants for 3-manifolds derived from supergroup representations.

We provide a calculus for the presentation of closed 3-manifolds via nullhomotopic filling Dehn spheres and we use it to define an invariant of closed 3-manifolds by applying the state-sum machinery. As a potential application of this invariant, we show how to get lower bounds for the Matveev complexity of P2-irreducib…

Homeomorphisms of hyperbolic 3-manifolds have invariant sets under certain conditions.

Infinite families of quantum modular invariants for 3-manifolds are discovered.

The paper defines and analyzes a volume invariant for 3-manifolds.

Paper develops techniques to create 3-manifold invariants.

Define mass invariant for asymptotically hyperbolic 3-manifolds with toroidal infinity.

Defines a new version of Turaev-Viro invariants for 3-manifolds with boundaries.

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

Invariant for 3-manifolds with torus boundary defined.

This is a list of open problems on invariants of knots and 3-manifolds with expositions of their history, background, significance, or importance. This list was made by editing open problems given in problem sessions in the workshop and seminars on `Invariants of Knots and 3-Manifolds' held at Kyoto in 2001.

Extends Milnor's invariants to knots and links in 3-manifolds.

New invariants defined for volume-preserving flows on 3-manifolds.

The paper proves an asymptotic additivity of Turaev-Viro invariants for a family of 3-manifolds.

We investigate the conjectural relations between the Reshetikhin-Turaev-Witten quantum SU(2) invariants and the volume of hyperbolic 3-manifolds. Given a finite set of sufficiently large positive integers, say J, we construct examples of closed hyperbolic 3-manifolds with the same invariants at all levels in J and diff…