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DOI:10.2140/AGT.2012.12.1607 - Corpus ID: 6714949
@article{Bardakov2009BRUNNIANBO, title={BRUNNIAN BRAIDS ON SURFACES}, author={Valery Bardakov and Roman Mikhailov and Vladimir V. Vershinin and Jie Wu}, journal={Algebraic \& Geometric Topology}, year={2009}, volume={12}, pages={1607-1648}, url={https://api.semanticscholar.org/CorpusID:6714949}}- V. Bardakov, Roman Mikhailov, Jie Wu
- Published 18 September 2009
- Mathematics
- Algebraic & Geometric Topology
In this article, we determine a set of generators for the Brunnian braids on a general surface M for M 6 S 2 or RP 2 . For the case M = S 2 or RP 2 , a set of generators for the Brun- nian braids on M is given by our generating set together with the hom*otopy groups of a 2-sphere.
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20 Citations
- P. Akhmet’ev
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An approach by J.Wu describes hom*otopy groups πn(S2) of the standard 2-sphere as isotopy classes of spherical n+1--strand Brunnian braids. The case n=3 is investigated for applications.
- A. BerrickE. HanburyJie Wu
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This is the second of a pair of papers on the Delta‐group structure on the braid and mapping class groups of a surface. We obtain a description of the hom*otopy groups of these Delta‐groups and…
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- Fengchun LeiJie WuYu Zhang
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Let G.Ln/ be the link group of a Brunnian n–link Ln and Ri be the normal closure of the i th meridian in G.Ln/ for 1 i n . In this article, we show that the intersecting subgroup R1 \R2 \ \Rm…
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- V. BardakovV. VershininJie Wu
- 2013
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For a general connected surface M and an arbitrary braid α from the surface braid group Bn−1(M), we study the system of equations d1β = … = dnβ = α, where the operation di is the removal of the ith…
- V. BardakovV. VershininJ. Wu
- 2014
Mathematics
Proceedings of the Steklov Institute of…
For a general connected surface M and an arbitrary braid α from the surface braid group Bn−1(M), we study the system of equations d1β = … = dnβ = α, where the operation di is the removal of the ith…
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By exploring simplicial structure of pure virtual braid groups, we give new connections between the hom*otopy groups of the 3-sphere and the virtual braid groups that are related to the theory of…
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We present and discuss some open problems formulated by participants of the International Workshop "Knots, Braids, and Auto\-mor\-phism Groups" held in Novosibirsk, 2014. Problems are related to…
- A. BerrickE. HanburyJie Wu
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We describe a Delta-group structure on the mapping class groups of surfaces, and show that it is compatible with the Delta-group structures of the braid groups of surfaces given by…
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- LI J.-Y.G. ×Gn−kWU J.
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In this paper, we investigate some applications of commutator subgroups to hom*otopy groups and geometric groups. In particular, we show that the intersection subgroups of some canonical subgroups in…
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33 References
- Jie Wu
- 2001
Mathematics
By studying braid group actions on Milnor’s construction of the 1sphere, we show that the general higher hom*otopy group of the 3-sphere is the fixed set of the pure braid group action on certain…
- 11
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- Jie WuJ. BerrickNaF. CohenY. Wong
- 2005
Mathematics
The main results of this article are certain connections between braid groups and the hom*otopy groups of the 2-sphere. The connections are given in terms of Brunnian braids over the disk and over the…
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- Jingyan LiJie Wu
- 2009
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We study the Brunnian subgroups and the boundary Brunnian subgroups of the Artin braid groups. The general higher hom*otopy groups of the sphere are given by mirror symmetric elements in the quotient…
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- D. L. Johnson
- 1982
Mathematics
Mathematical Proceedings of the Cambridge…
The braid group on n + 1 strings has the presentation where xi corresponds to the single crossing of the i string over the i + 1 string, and rij is a commutator when i < j − 1, and a braid relator…
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- R. MikhailovI. PassiJie Wu
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- Jie Wu
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Mathematical Proceedings of the Cambridge…
We give a combinatorial description of the hom*otopy groups of the suspension of a K(π, 1) and of wedges of 2-spheres. In particular, all of the hom*otopy groups of the 2-sphere are given as the…
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