Braid groups and the group of homeomorphisms of a surface

1 November 1970

journal article
research article
Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society

Vol. 68 (3) , 605-617
https://doi.org/10.1017/s0305004100076593

Abstract

Braid groups on the plane were denned by Artin(1) in 1925. More recently Fox(8) defined braid groups on arbitrary topological spaces, the situation being particularly interesting if the space is a 2-manifold. Presentations of the braid groups on R2, S2 and P2 can be found in (2), (6) and (13) respectively, and some general results on braid groups of compact 2-manifolds can be found in (7). In section 1 of this paper, we give finite presentations for the braid groups on all closed 2-manifolds except S2 and P2.

Keywords

BRAID GROUP

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