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 ...
6
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1answer
834 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 ...
4
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1answer
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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 $V$ ...
7
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1answer
458 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 ...