Braid groups in handlebodies and corresponding Hecke algebras
Abstract
In this paper we study the kernel of the homomorphism $B_{g,n} \to B_n$ 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 $B_n$.
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2017
- DOI:
- 10.48550/arXiv.1701.03631
- arXiv:
- arXiv:1701.03631
- Bibcode:
- 2017arXiv170103631B
- Keywords:
-
- Mathematics - Group Theory;
- Mathematics - Geometric Topology;
- 20F36;
- 20E05
- E-Print:
- 15 pages, corrected versiov