Related papers: Torus bundles not distinguished by TQFT invariants

In this paper we show how one can extend Turaev-Viro invariants, defined for an arbitrary spherical fusion category $C$, to 3-manifolds with corners. We demonstrate that this gives an extended TQFT which conjecturally coincides with the…

By methods similar to those used by Lisa Jeffrey, we compute the quantum $\mathrm{SU}(N)$-invariants for mapping tori of trace $2$ homeomorphisms of a genus $1$ surface when $N = 2,3$ and discuss their asymptotics. In particular, we obtain…

In this paper we consider the representation theory of a non-standard quantization of sl(2). This paper contains several results which have applications in quantum topology, including the classification of projective indecomposable modules…

We define a once extended non-compact 3-dimensional TQFT $\mathcal{Z}$ from the data of a (potentially) non-semisimple modular tensor category. This is in the framework of generators and relations of [Bartlett et al., arxiv:1509.06811…

We construct several examples of (2+1) dimensional N=2 supersymmetric Chern-Simons theories, whose moduli space is given by non-compact toric Calabi-Yau four-folds, which are not derivable from any (3+1) dimensional CFT. One such example is…

Supermembrane compactified on a $M_9\times T^2$ target space is globally described by the inequivalent classes of torus bundles over torus. These torus bundles have monodromy in $SL(2,Z)$ when they correspond to the nontrivial central…

In this article we give examples which show that the TQFT representations of the mapping class groups derived from quantum SU(N) for N>2 are generically decomposable. One general decomposition of the representations is induced by the…

We define a torsion invariant T for every balanced sutured manifold (M,g), and show that it agrees with the Euler characteristic of sutured Floer homology SFH. The invariant T is easily computed using Fox calculus. With the help of T, we…

We prove that the Turaev--Viro invariants of the two surface bundles over the circle coincide for every spherical fusion category if the surface group is procongruently conjugacy separable and there exists a regular profinite isomorphism…

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…

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…

It is known that the T-dual of a circle bundle with H-flux (given by a Neveu-Schwarz 3-form) is the T-dual circle bundle with dual H-flux. However, it is also known that torus bundles with H-flux do not necessarily have a T-dual which is a…

We prove that every holomorphic vector bundle on a noncommutative two-torus $T$ can be obtained by successive extensions from standard holomorphic bundles considered in math.QA/0211262. This implies that the category of holomorphic bundles…

We present an explicit expression for the topological invariants associated to $SU(2)$ monopoles in the fundamental representation on spin four-manifolds. The computation of these invariants is based on the analysis of their corresponding…

We define a nontrivial mod 2 valued additive concordance invariant defined on the torsion subgroup of the knot concordance group using involutive knot Floer package. For knots not contained in its kernel, we prove that their iterated…

We construct families of TQFT's over the finite field Z/pZ starting from an integral TQFT obtained by Frohman and Nicas. These TQFT's are likely to describe the constant order contributions of the cyclotomic integer expansions of the…

Computing topological invariants of 3-manifolds is generally intractable, yet specialized algebraic structures can enable efficient algorithms. For Witten-Reshetikhin-Turaev (WRT) invariants of torus bundles, we exploit the non-commutative…

Drinfeld doubles of finite subgroups of SU(2) and SU(3) are investigated in detail. Their modular data - S, T and fusion matrices - are computed explicitly, and illustrated by means of fusion graphs. This allows us to reexamine certain…

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…

We introduce the 3-alterfold topological quantum field theory (TQFT) by extending the quantum invariant of 3-alterfolds. The bases of the TQFT are explicitly characterized and the Levin-Wen model is naturally interpreted in 3-alterfold TQFT…