Finite-type (Vassiliev) invariants, quantum invariants, and perturbative invariants of knotted objects and of manifolds.

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Why hasn't anyone proved that the two standard approaches to quantizing Chern-Simons theory are equivalent?

The two standard approaches to the quantization of Chern-Simons theory are geometric quantization of character varieties, and quantum groups plus skein theory. These two approaches were both first ...
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Why do people study representations of 3-manifold groups into $SL(n,\mathbb{C})$?

Varieties of representations and characters of $3$-manifold groups in $SL(2,\mathbb{C})$ have been intensively studied. They have provided tools to identify geometric structures on manifolds, and are ...
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955 views

Why Lagrangian cobordism?

There are a good number of quantum topology papers in which a TQFT-like set-up is constructed as a functor to the category of vector spaces from some category of cobordisms which satisfy some "...
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Quantization of symplectic vector space and choice of lagrangian subspaces

My question is related to Geometric Quantization. I don't undrestand the philosophy of following assertion If $(V,\omega)$ be a symplectic vector space then the quantizations of $V$ ...
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524 views

Diagrammatic proof of unique prime decomposition of knots

Consider a knot to be a diagram in a plane--- i.e. a drawing of a finite connected planar graph (loops and multiple edges allowed) whose vertices are 4-valent with cyclic ordering for the incident ...
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Brauer-Picard for a fusion category coming from a quantum group

In Fusion Categories and Homotopy Theory, ENO attatch a 3-groupoid to a fusion category. In the case of A graded vector spaces they further compute it's truncation as an orthogonal group $O(A \...
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217 views

Invariants of unframed, oriented links from Reshetikhin Turaev construction

Hello! I have a few questions on Reshetikhin Turaev invariants. By RT any ribbon category ${\mathcal C}$ yields an invariant of oriented, framed links labelled with objects of ${\mathcal C}$. Is ...
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477 views

Now that I got a mutant-discriminating invariant…

...what can I do with the darn thing? Background: I read that still no Vassiliev Invariant with mutant-discriminating power is known (correct me if this is outdated). Now, my research lead to a whole ...