Geodesic
Matrix model and dimensions at hypercube vertices
Teoretičeskaâ i matematičeskaâ fizika, Tome 192 (2017) no. 1, pp. 115-163

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We consider correlation functions in the Chern–Simons theory (knot polynomials) using an approach in which each knot diagram is associated with a hypercube. The number of cycles into which the link diagram is decomposed under different resolutions plays a central role. Certain functions of these numbers are further interpreted as dimensions of graded spaces associated with hypercube vertices, but finding these functions is a somewhat nontrivial problem. It was previously suggested to solve this problem using the matrix model technique by analogy with topological recursion. We develop this idea and provide a wide collection of nontrivial examples related to both ordinary and virtual knots and links. The most powerful version of the formalism freely connects ordinary knots/links with virtual ones. Moreover, it allows going beyond the limits of the knot-related set of $(2,2)$-valent graphs.
Keywords: Chern–Simons theory, knot theory, virtual knot, matrix model. 
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     author = {A. Yu. Morozov and A. A. Morozov and A. V. Popolitov},
     title = {Matrix model and dimensions at hypercube vertices},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {192},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2017_192_1_a7/}
}
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A. Yu. Morozov; A. A. Morozov; A. V. Popolitov. Matrix model and dimensions at hypercube vertices. Teoretičeskaâ i matematičeskaâ fizika, Tome 192 (2017) no. 1, pp. 115-163. http://geodesic.mathdoc.fr/item/TMF_2017_192_1_a7/