Geodesic
Fibonacci representations of braid groups
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 30 (2024) no. 4, pp. 149-169 Cet article a éte moissonné depuis la source Math-Net.Ru

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A family of representations is constructed for the braid group $B_n$. The vector spaces on which the braid group acts are defined as the result of identifying the spaces generated by proper colorings of regular trees of degree $3$ with a marked vertex. This identification is done using a family of canonical isomorphisms. The dimensions of the resulting spaces form the sequence of Fibonacci numbers. We then show how the constructed representations can be extended to invariants of unoriented knots and links in a 3-sphere.
Keywords: braid group, representation, knot invariant, Reshetikhin–Turaev type invariant. 
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Ph. G. Korablev. Fibonacci representations of braid groups. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 30 (2024) no. 4, pp. 149-169. http://geodesic.mathdoc.fr/item/TIMM_2024_30_4_a11/

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