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Results tagged with topological-quantum-field-theory
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user 119012
Topological quantum field theory.
1
vote
0
answers
71
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Reshetikhin-Turaev invariants from extended 3d TQFTs
Attached to any object $V\in \mathcal{C}$ of a ribbon category $\mathcal{C}$, Reshetikhin and Turaev have defined knot invariants
$$\tau_V(K)\ \in\ \text{End}_{\mathcal{C}}(1_{\mathcal{C}})$$
for inst …
- 5,701
6
votes
1
answer
513
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Defining extended TQFTs *with point, line, surface, … operators*
$\newcommand\Cob{\mathrm{Cob}}\newcommand\Vect{\mathrm{Vect}}\DeclareMathOperator\Rep{Rep}$The ordinary definition of a TQFT is:
Defnition: A $d$-dimensional TQFT is a symmetric monoidal functor $\Cob …
- 5,701
8
votes
0
answers
230
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$U_q(\mathfrak{g})$ is to knot theory as $U_q(\hat{\mathfrak{g}})$ is to $?$
Let $\mathfrak{g}$ be a finite dimensional semisimple Lie algebra over the complex numbers, e.g. $\mathfrak{sl}_n$.
Then every representation $\DeclareMathOperator\Rep{Rep}V\in \Rep U_q(\mathfrak{g})$ …
- 5,701
12
votes
0
answers
426
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What is the motivation for a Frobenius manifold?
A Frobenius manifold is a type of manifolds with extra structure.
The main examples are quantum cohomology (viewed as a space itself), GBV algebras, the ``Saito'' examples arising from singularities ( …
- 5,701