Matrix model and dimensions at hypercube vertices

Matrix model and dimensions at hypercube vertices 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. Theoretical and Mathematical Physics Springer Journals

Matrix model and dimensions at hypercube vertices

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Pleiades Publishing
Copyright © 2017 by Pleiades Publishing, Ltd.
Physics; Theoretical, Mathematical and Computational Physics; Applications of Mathematics
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