Related papers: The volume and Chern-Simons invariant of a represe…

We construct an invariant of 3-manifolds using a modification of the Kontsevich integral and Kirby's calculus. This invariant, as expected in perturbative Chern-Simon theory, takes values in the algebra of oriented 3-valent graphs. This…

In this paper, we find lower bounds for volumes of hyperbolic 3-manifolds with various topological conditions. Let V_3 = 1.01494 denote the volume of a regular ideal simplex in hyperbolic 3-space. As a special case of the main theorem, if a…

In this paper we present a torsional non-relativistic Chern-Simons teleparallel (super)gravity theory in three spacetime dimensions. We start by developing the non-relativistic limit of the purely bosonic relativistic teleparallel…

We consider the relation between simplicial volume and two of its variants: the stable integral simplicial volume and the integral foliated simplicial volume. The definition of the latter depends on a choice of a measure preserving action…

The present paper considers volume formulae, as well as trigonometric identities, that hold for a tetrahedron in 3-dimensional spherical space of constant sectional curvature +1. The tetrahedron possesses a certain symmetry: namely rotation…

A simplified model for a planet's atmosphere as an open two-dimensional Chern-Simons system is presented. The dynamical variables describe an ideal gas by its velocity, mass density, temperature and pressure. Radiation exchange, diffusion…

Building on Hitchin's work of the Wess-Zumino-Witten term for harmonic maps into Lie groups, we derive a formula for the enclosed volume of a compact CMC surface $f$ in $\mathbb S^3$ in terms of a holonomy on the Chern-Simons bundle and the…

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 consider the Witten-Reshetikhin-Turaev invariants or Chern-Simons partition function at or around roots of unity $q=e^{2\pi i \frac{1}{K}}$ with rational level $K=\frac{r}{s}$ where $r$ and $s$ are coprime integers. From the exact…

We propose a finite dimensional variational principle on triangulated 3-manifolds so that its critical points are related to solutions to Thurston's gluing equation and Haken's normal surface equation. The action functional is the volume.…

Let $M$ be a hyperbolizable $3$-manifold with boundary, and let $\chi_0(M)$ be a component of the $PSL_2\mathbb{C}$-character variety of $M$ that contains the convex co-compact characters. We show that the peripheral map…

The Chern-Simons exact solution of four-dimensional quantum gravity with nonvanishing cosmological constant is presented in metric variable as the partition function of a Chern-Simons theory with nontrivial source. The perturbative…

We study Chern-Simons theory on 3-manifolds M that are circle-bundles over 2-dimensional orbifolds S by the method of Abelianisation. This method, which completely sidesteps the issue of having to integrate over the moduli space of…

In this paper, we show that Gromov-Thurston's principle works for hyperbolic 3-manifolds of infinite volume and with finitely generated fundamental group. As an application, we have a new proof of Ending Lamination Theorem. Our proof…

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…

In this paper the hamiltonian analysis of the pure Chern-Simons theory on the noncommutative plane is performed. We use the techniques of geometric quantization to show that the classical reduced phase space of the theory has nontrivial…

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…

We define an invariant, which we call surface-complexity, of compact 3-manifolds by means of Dehn surfaces. The surface-complexity is a natural number measuring how much the manifold is complicated. We prove that it fulfils interesting…

We discuss Stochastic Quantization of $d$=3 dimensional non-Abelian Chern-Simons theory. We demonstrate that the introduction of an appropriate regulator in the Langevin equation yields a well-defined equilibrium limit, thus leading to the…

For closed and oriented hyperbolic surfaces, a formula of Witten establishes an equality between two volume forms on the space of representations of the surface in a semisimple Lie group. One of the forms is a Reidemeister torsion, the…