Journal ArticleDOI
Braid groups and the group of homeomorphisms of a surface
G. P. Scott
- Vol. 68, Iss: 3, pp 605-617
TLDR
In this article, the authors give finite presentations for the braid groups on all closed 2-manifolds except S2 and P2, and show that they can be found on R2, S2, P2 and S2.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.read more
Citations
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Invariants of $3$-manifolds and projective representations of mapping class groups via quantum groups at roots of unity
TL;DR: In this article, a finite dimensional factorizable ribbon Hopf ℂ-algebra is given by a quotient of the quantized universal enveloping algebra at a root of unityq of odd degree.
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Why are braids orderable
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The topology of rational functions and divisors of surfaces
TL;DR: In this article, the homotopy types of the spaces of holomorphic functions of the 2-sphere S 2, of closed surfaces of higher genus, and of divisors of these surfaces were studied.
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On presentations of surface braid groups
TL;DR: In this article, the authors give a presentation of braid groups and pure braid group on surfaces and show some properties of surface pure Braid groups, and show that pure BRAB groups have some properties similar to those of pure pure bRAB.
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Geometric subgroups of surface braid groups
Luis Paris,Dale Rolfsen +1 more
TL;DR: In this paper, the conditions générales d'utilisation (http://www.numdam.org/conditions) are defined, i.e., toute utilisation commerciale ou impression systématique is constitutive d'une infraction pénale.
References
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Journal ArticleDOI
Theory of Braids
TL;DR: A theory of braids leading to a classification was given in my paper "Theorie der Zopfe" in vol.
Journal Article
The theory of braids.
TL;DR: The theory of braids as discussed by the authors shows the interplay of two disciplines of pure mathematics? topology, used in the definition of Braids, and the theory of groups used in their treatment.