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Results tagged with extended-tqft
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user 13767
8
votes
1
answer
350
views
Does the notion of a "coherent state" exist in TQFTs? (ETQFTs?)
In the quantum harmonic oscillator, there exists a family of states called coherent states which form an overcomplete set of states. They are regarded as "the states most resembling classical states", …
- 5,565
10
votes
1
answer
274
views
Are there 4d state sum models, extended TQFTs or chain mail invariant that detect smooth str...
A state sum model is a smooth invariant defined on smooth triangulated, or PL manifolds, by summing a local partition function over labels attached to the elements of the triangulation.
Typical exampl …
- 5,565
5
votes
0
answers
238
views
(∞,n)-category of triangulated cobordisms
What is an accepted definition of a (∞,n)-category of triangulated cobordisms?
Is there one that has a forgetful functor to (Rezk - Hopkins -) Lurie's smooth cobordisms? Does it shed light on how Tur …
- 5,565
7
votes
0
answers
453
views
Is there a higher, "orientalish" version of geometric realisation?
Geometric realisation of simplicial sets can be roughly thought of like this:
In some category $\mathcal{C}$, we choose an object for every abstract $n$-simplex. In topological spaces, we would choo …
- 5,565
8
votes
0
answers
370
views
Is there a classification of 2d extended TQFTs with defects?
Chris Schommer-Pries has classified 2d extended TQFTs (topological quantum field theories) in his PhD thesis. The result is a (not necessarily abelian) separable symmetric Frobenius algebra (possibly …
- 5,565
9
votes
1
answer
639
views
Is Turaev-Viro-Barrett-Westbury stronger than homotopy?
I've heard that Reshetikhin-Turaev (RT) is stronger than homotopy, and it can distinguish certain homotopy-equivalent, but non-homeomorphic Lens spaces (I think $L(7,1)$ and $L(7,2)$). Now the Turaev- …
- 5,565
14
votes
1
answer
647
views
Is there a PL, or topological, bordism hypothesis?
The bordism hypothesis says that the $(\infty, n)$-category of smooth, framed $n$-bordisms, $(n-1)$-dimensional boundaries, and corners down to points, is freely generated symmetric monoidal with dual …
- 5,565