R-matrix knot invariants and triangulations
R. M. Kashaev
TL;DR
This paper reviews how quantum knot invariants derived from R-matrices, solutions to the Yang-Baxter equation, can be understood through three-dimensional geometric interpretations.
Contribution
It introduces a class of R-matrices that allow for an intrinsic three-dimensional understanding of quantum knot invariants.
Findings
Identification of R-matrices with 3D geometric meaning
Connection between Yang-Baxter solutions and knot invariants
Enhanced understanding of quantum invariants in 3D context
Abstract
The construction of quantum knot invariants from solutions of the Yang--Baxter equation (R-matrices) is reviewed with the emphasis on a class of R-matrices admitting an interpretation in intrinsically three-dimensional terms.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Geometric and Algebraic Topology · Advanced Topics in Algebra