# 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Theoretical and Mathematical Physics Springer Journals

# Matrix model and dimensions at hypercube vertices

, Volume 192 (1) – Aug 15, 2017
41 pages

/lp/springer_journal/matrix-model-and-dimensions-at-hypercube-vertices-009veb3BDo
Publisher
Springer Journals
Subject
Physics; Theoretical, Mathematical and Computational Physics; Applications of Mathematics
ISSN
0040-5779
eISSN
1573-9333
D.O.I.
10.1134/S004057791707008X
Publisher site
See Article on Publisher Site

### Abstract

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.

### Journal

Theoretical and Mathematical PhysicsSpringer Journals

Published: Aug 15, 2017

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