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

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633 views

Is there an “arithmetic cobordism category”?

This question is a clumsy attempt to apply a certain analogy. I hope that if the answer is negative it comes with a clarification of the scope and limitations of the analogy. Arithmetic topology is ...
9
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239 views

Provide a citation for the “spine lemma”?

I'm looking for a citable reference for the following (perhaps folkloric?) result on topological field theories. (There are obviously generalizations to other dimensions; I'm happy with just the ...
9
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399 views

Representations of quantum groups at roots of unity

I'm interested in the semisimplified category of representations of a quantum group at a root of unity. I've heard that simple objects in this category correspond to certain "integral" conjugacy ...
8
votes
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277 views

Which presentations of (non)planar algebras give rise to knots?

Reidermeister's theorem states that the set of knots, modulo ambient isotopy, is isomorphic to the planar algebra generated by crossings, modulo Reidemeister moves. This planar algebra presentation is ...
5
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127 views

Construction of 3D Topological Quantum Field Theory from a 2D Modular Functor

I have been reading Bakalov and Kirillov's Lectures on Tensor Categories and Modular Functors in which the authors state that a direct construction of a $C$-extended 3D TQFT from a $C$-extended 2D ...
5
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221 views

generators for Hecke algebra quotients

What are generators for the kernel of the (k,r)-quotient of the Hecke algebras of type A? Are just the two projections onto the reps. corresponding to Young digarams with 1-row of length r-k+1 and ...
4
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140 views

S-matrix for the BMW category

This question concerns the Birman-Murakami-Wenzl category, or equivalently the tangle category associated to the 2-variable Kauffman polynomial. (See here for example.) The minimal idempotents of ...
3
votes
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123 views

Is a generic link diagram semi-adequate?

Each crossing in a link diagram of a link $L$ has an A-resolution and a B-resolution. Resolving all crossings gives a collection of circles in the plane, connected by dotted lines. A state of a ...
3
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264 views

On finding A-polynomials

I have two questions to obtain the explicit forms of A-polynomials. Takata used the mathematica pacage qMultisum.m to obtain the recursion relation of the colored Jones polynomials for twist knots. ...