Braid groups in handlebodies and corresponding Hecke algebras

DOI10.1007/978-3-319-68103-0_9zbMATH Open1406.20043arXiv1701.03631OpenAlexW2963327709MaRDI QIDQ1697072

Valeriy G. Bardakov

Publication date: 15 February 2018

Abstract: In this paper we study the kernel of the homomorphism $B_{g,n}o{B}_n$ of the braid group $B_{g,n}$ in the handlebody $mathcal{H}_g$ to the braid group $B_n$. We prove that this kernel is a semi-direct product of free groups. Also, we introduce an algebra $H_{g,n}(q)$, which is some analog of the Hecke algebra $H_n(q)$, constructed by the braid group $B_n$.

Full work available at URL: https://arxiv.org/abs/1701.03631

Mathematics Subject Classification ID

Hecke algebras and their representations (20C08) Braid groups; Artin groups (20F36)

Related Items (4)

Unnamed Item ⋮ Unnamed Item ⋮ Handlebody diagram algebras ⋮ Surface braid groups, Finite Heisenberg covers and double Kodaira fibrations

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