相关论文: On the relation between the WRT invariant and the …
We show that the Witten-Reshetikhin-Turaev SU(2) invariant and the Hennings invariant associated to the restricted quantum $sl_2$ are essentially the same for rational homology 3-spheres.
The Witten-Reshetikhin-Turaev invariants extend the Jones polynomials of links in S^3 to invariants of links in 3-manifolds. Similarly, in a preceding paper, the authors constructed two 3-manifold invariants N_r and N^0_r which extend the…
The Hennings invariant for the small quantum group associated to an arbitrary simple Lie algebra at a root of unity is shown to agree with Jones- Witten-Reshetikhin-Turaev invariant arising from Chern-Simons filed theory for the same Lie…
In this thesis, we give a unification of the quantum WRT invariants. Given a rational homology 3-sphere M and a link L inside, we define the unified invariants, such that the evaluation of these invariants at a root of unity equals the…
The computational complexity class #P captures the difficulty of counting the satisfying assignments to a boolean formula. In this work, we use basic tools from quantum computation to give a proof that the SO(3) Witten-Reshetikhin-Turaev…
In this paper we construct a topological model for the Witten-Reshetikhin-Turaev invariants for $3$-manifolds coming from the quantum group $U_q(sl(2))$, as graded intersection pairings of homology classes in configuration spaces. More…
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 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…
We present a relation between the Witt invariants of 3-manifolds and the $\hat{Z}$-invariants. It provides an alternative approach to compute the Witt invariants of 3-manifolds, which were originally defined geometrically in four…
For every rational homology 3-sphere with 2-torsion only we construct a unified invariant (which takes values in a certain cyclotomic completion of a polynomial ring), such that the evaluation of this invariant at any odd root of unity…
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…
We prove that the Witten-Reshetikhin-Turaev (WRT) SO(3) invariant of an arbitrary 3-manifold M is always an algebraic integer. Moreover, we give a rational surgery formula for the unified invariant dominating WRT SO(3) invariants of…
We study the SU(2) Witten--Reshetikhin--Turaev invariant for the Seifert fibered homology spheres with M-exceptional fibers. We show that the WRT invariant can be written in terms of (differential of) the Eichler integrals of modular forms…
We prove a 20-year-old conjecture concerning two quantum invariants of three manifolds that are constructed from finite dimensional Hopf algebras, namely, the Kuperberg invariant and the Hennings-Kauffman-Radford invariant. The two…
We study the relations between the invariants $\tau_{RT}$, $\tau_{HKR}$, and $\tau_L$ of Reshetikhin-Turaev, Hennings-Kauffman-Radford, and Lyubashenko, respectively. In particular, we discuss explicitly how $\tau_L$ specializes to…
We will announce some results on the values of quantum sl_2 invariants of knots and integral homology spheres. Lawrence's universal sl_2 invariant of knots takes values in a fairly small subalgebra of the center of the h-adic version of the…
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…
In 2006 Habiro initiated a construction of generating functions for Witten-Reshetikhin-Turaev (WRT) invariants known as unified WRT invariants. In a series of papers together with Irmgard Buehler and Christian Blanchet we extended his…
We recover the family of non-semisimple quantum invariants of closed oriented 3-manifolds associated with the small quantum group of $\mathfrak{sl}_2$ using purely combinatorial methods based on Temperley-Lieb algebras and Kauffman bracket…
The values of the Witten invariants, $I_W$, of the lens space $L(p, 1)$ for SU(2) at level $k$ are obtained for arbitrary $p$. A duality relation for $I_W$ when $p$ and $k$ are interchanged, valid for asymptotic $k$, is observed. A method…