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A geometric interpretation of the normal closure of the braid group $B_{n}$ in the braid group of the torus $B_{n} (T)$

Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012 USA

https://doi.org/10.1142/S021821651950038XCited by:0 (Source: Crossref)

Abstract

It had been proved by Birman and Goldberg that the normal closure of the pure braid group $P_{n} (D)$ in the pure braid group of the torus $P_{n} (T)$ is the commutator subgroup $[P_{n} (T), P_{n} (T)]$ . In this paper, we are going to study the case of full braid groups: i.e. the normal closure of $B_{n} (D)$ in $B_{n} (T)$ , which turns out to have an interesting geometric description.

Keywords:

AMSC: 57M07, 20F36

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