Related papers: Three Manifolds and Graph Invariants

We propose a program for bridging the gap between the perturbative BV-BFV quantization of Chern-Simons theory and the non-perturbative Reshetikhin-Turaev (RT) invariants of 3-manifolds, passing through factorization homology of…

We study the Witten--Reshetikhin--Turaev SU(2) invariant for the Seifert manifold $S^3/\Gamma$ where $\Gamma$ is a finite subgroup of SU(2). We show that the WRT invariants can be written in terms of the Eichler integral of the modular…

We construct and study a new topological field theory in three dimensions. It is a hybrid between Chern-Simons and Rozansky-Witten theory and can be regarded as a topologically-twisted version of the N=4 d=3 supersymmetric gauge theory…

Sinha and Vafa had conjectured that the $SO$ Chern-Simons gauge theory on $S^3$ must be dual to the closed $A$-model topological string on the orientifold of a resolved conifold. Though the Chern-Simons free energy could be rewritten in…

In this paper, we discuss relations among several invariants of 3-manifolds including Meyer's function, the eta-invariant, the von Neumann rho-invariant and the Casson invariant from the viewpoint of the mapping class group of a surface.

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…

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.…

We study globally supersymmetric 3d gauge theories on curved manifolds by describing the coupling of 3d topological gauge theories, with both Yang-Mills and Chern-Simons terms in the action, to background topological gravity. In our…

For a system of ODEs defined on an open, convex domain $U$ containing a positively invariant set $\Gamma$, we prove that under appropriate hypotheses, $\Gamma$ is the graph of a $C^r$ function and thus a $C^r$ manifold. Because the…

The 3D-index of Dimofte-Gaiotto-Gukov is an interesting collection of $q$-series with integer coefficients parametrised by a pair of integers and associated to a 3-manifold with torus boundary. In this note, we explain the structure of the…

We study the quantum mechanics of a system of topologically interacting particles in 2+1 dimensions, which is described by coupling the particles to a Chern-Simons gauge field of an inhomogeneous group. Analysis of the phase space shows…

We consider analytic maps and vector fields defined in $\mathbb{R}^2 \times \mathbb{T}^d$, having a $d$-dimensional invariant torus $\mathcal{T}$. The map (resp. vector field) restricted to $\mathcal{T}$ defines a rotation of frequency…

In their recent work, Garoufalidis and Kashaev extended the 3D-index of an ideally triangulated 3-manifold with toroidal boundary to a well-defined topological invariant which takes the form of a meromorphic function of 2 complex variables…

We derive an explicit formula for the Witten-Reshetikhin-Turaev SO(3)-invariants of lens spaces. We use the representation of the mapping class group of the torus corresponding to the Witten-Reshetikhin-Turaev SO(3)-TQFT to give such…

Chern-Simons field theory based on a compact non-abelian gauge group is studied as a theory of knots and links in three dimensions. A method to obtain the invariants for links made from braids of upto four strands is developed. This…

We report on recent results of the authors concerning calculations of quantum invariants of Seifert 3-manifolds. These results include a derivation of the Reshetikhin-Turaev invariants of all oriented Seifert manifolds associated with an…

Khovanov homology is an invariant for links in the three sphere that categorizes the Jones polynomial. We extend Khovanov's construction to links in 3-manifolds that are connected sums of orientable interval bundles over surfaces. Cutting…

The triple point numbers and the triple point spectrum of a closed 3-manifold were defined in (R. Vigara, Representaci\'on de 3-variedades por esferas de Dehn rellenantes, PhD Thesis, UNED 2006). They are topological invariants that give a…

Suppose $\Gamma$ is a discrete group, and $\alpha\in Z^3(B\Gamma;A)$, with $A$ an abelian group. Given a representation $\rho:\pi_1(M)\to\Gamma$, with $M$ a closed 3-manifold, put $F(M,\rho)=\langle(B\rho)^\ast[\alpha],[M]\rangle$, where…

The level-k U(1) Chern-Simons theory is a spin topological quantum field theory for k odd. Its dynamics is captured by the 2d CFT of a compact boson with a certain radius. Recently it was recognized that a dependence on the 2d spin…