In his book Quantum invariants of knots and 3-manifolds page 124, Turaev defined a TQFT $\tau$ axiomatically. For a cobordism $(M, \partial_{-}M, \partial_{+}M)$, a TQFT assignes …

Say I have an "ordinary" TQFT $F$ of dimension $n$, assigning groups or vector spaces to closed $(n-1)$-manifolds and linear maps to cobordisms. Consider the different ways $F$ can …

This is a reference request. I'm looking for a definition of Morita equivalence of *-algebras, as described below. If anyone thinks that this is not the right way to define Morit …

In an extended 2d TQFT $Z$, a point (with orientation + or -) is assigned a category $Z(+)$ or $Z(-)$. This category should be as close to a vector space as possible: $\mathbb{C}$- …

Let $G$ be a finite group. Usually, a 2-cocycle on $G$ with values in $\mathbb{Z}_2 = \{+1, -1\}$ is a collection of signs $\epsilon_{g,h} \in \{+1, -1\}$, $g,h \in G$, satisfying …

Question: Is there a condition on an object $x$ of an $(\infty,2)$-category $\mathcal C$ which is equivalent to $x = Z(pt_+)$ for a unique TFT $Z$ from the $(\infty,2)$-category of …

I have been studying topological quantum field theory by mainly reading the Turaev's book. I'd like to know if there are unsolved problems that motivate mathematicians to study TQ …

Hi, this is my first post here, so I hope I am asking the question the right way. I am trying to understand to following piece of algebra: In his paper, Witten claims that $\int_M …

I posted the following question on math stackexchange but I have not received any answer. So I hope people here can help me. In the book, Lectures on tensor categories and modular …

I am studying Turaev-Reshetikhin TQFT. I describe the definition of the invariant $\tau(M)$ of a cobordism $(M, \partial_{-}M, \partial_{+}M)$ in the previous question breifly. htt …

This question concerns the HOMFLY-PT category, closely related to Hecke algebras. (See here for example.) The minimal idempotents of this category are indexed by pairs $(\lambd …

Can you suggest a reading list, or at least a few papers that you think would be useful, for a beginner in topological quantum field theory? I know what the curvature of a connecti …

I posted the following question at Mathe Stack Exchange.link text But it has not yet answered. I am sorry if you check both sites but I also want people here to look at this proble …

I'm interested in the Witten-Reshetikhin-Turaev invariants for 3-manifolds, and in particular, how to calculate them from a triangulation of the 3-manifold (recall that as they wer …

I keep reading that the Reshetikhin-Turaev construction actually yields a 3-2-1 tqft. I know the construction that associates to a suitably decorated surface a vector space built u …