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Braid groups and the group of homeomorphisms of a surface

Published online by Cambridge University Press:  24 October 2008

G. P. Scott
G. P. Scott
Affiliation:
University of Liverpool
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Extract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 3 , November 1970 , pp. 605 - 617
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

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