Related papers: The Teichm\"uller TQFT
We construct a new infinite family of ideal triangulations and H-triangulations for the complements of twist knots, using a method originating from Thurston. These triangulations provide a new upper bound for the Matveev complexity of twist…
By using quantum Teichm\"uller theory, we construct a one parameter family of TQFT's on the categroid of admissible leveled shaped 3-manifolds.
We calculate the knot invariant coming from the Teichm\"{u}ller TQFT [AK1]. Specifically we calculate the knot invariant for the complement of the knot $6_1$ both in the original [AK1] and the new formulation of the Teichm\"{u}ller TQFT…
The quantization of the Teichm\"uller theory has led to the formulation of the so-called Teichm\"uller TQFT for 3-manifolds. In this paper we initiate the study of "supersymmetrization" of the Teichm\"uller TQFT, which we call the super…
By using the Weil-Gel'fand-Zak transform of Faddeev's quantum dilogarithm, we propose a new state-integral model for the Teichm\"uller TQFT, where the circle valued state variables live on the edges of oriented leveled shaped…
In this paper we propose a naive construction of 2-dimensional extended topological quantum field theories (TQFTs), which can be further generalized to the higher-dimension extended TQFTs.
The goal of this article is to invite the reader to get to know and to get involved into higher Teichm\"uller theory by describing some of its many facets.
In the generalized topological quantum field theory constructed by Andersen and Kashaev, invariants of 3-manifolds are defined given the combinatorial structure of a tetrahedral decomposition. Furthermore, a variant of the volume conjecture…
Recent works in quantum gravity, motivated by the factorization problem and baby universes, have considered sums over bordisms with fixed boundaries in topological quantum field theory (TQFT). We discuss this construction and observe a…
An earlier paper gave a means of calculating the Lamb shift via Feynman diagrams. Here we apply the same techniques to TQFT.
We give an overview over several constructions of TQFT's over finite fields and cyclotomic integers and their applications to characterizing 3-manifolds and their fundamental groups.
Teichm\"uller TQFT is a unitary 3d topological theory whose Hilbert spaces are spanned by Liouville conformal blocks. It is related but not identical to PSL(2,R) Chern-Simons theory. To physicists, it is known in particular in the context…
We construct two-dimensional non-commutative topological quantum field theories (TQFTs), one for each Hecke algebra corresponding to a finite Coxeter system. These TQFTs associate an invariant to each ciliated surface, which is a Laurent…
We recall the history of the proof of Seifert fibre space conjecture, as well as it motivations and its several generalisations.
I propose a new mathematical form for the quantum theory of gravity coupled to matter. The motivation is from the connection between CSW TQFT and the Ashtekar variables. I also connect the algebraic structure of TQFT with some thoughts…
We prove the volume conjecture for any twist knots by using an equivalence relation, complex analysis, analytic continuation, and function of several complex variables on the basis of colored Jones polynomials.
This is an invited contribution to the 2nd edition of the Encyclopedia of Mathematical Physics. We give an overview of 3-dimensional topological quantum field theories (TQFTs) and the corresponding quantum invariants of 3-manifolds. We…
We state a conjecture about the volume of symplectically self-polar convex bodies and show that it is equivalent to Mahler's conjecture concerning the volume of a convex body and its Euclidean polar. We also establish lower and upper bounds…
The aim of these lecture notes is, after having quickly described various compactifications of the Teichm\"{u}ller space of a compact connected oriented surface minus finitely many points, to give a construction, by the equivariant Gromov…
New cases of the multiplicity conjecture are considered.