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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On symmetric commutator subgroups, braids, links and homotopy groups


Authors: J. Y. Li and J. Wu
Journal: Trans. Amer. Math. Soc. 363 (2011), 3829-3852
MSC (2010): Primary 55Q40, 20F12; Secondary 20F36, 57M25
Published electronically: February 25, 2011
MathSciNet review: 2775829
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Abstract: In this paper, we investigate some applications of commutator subgroups to homotopy groups and geometric groups. In particular, we show that the intersection subgroups of some canonical subgroups in certain link groups modulo their symmetric commutator subgroups are isomorphic to the (higher) homotopy groups. This gives a connection between links and homotopy groups. Similar results hold for braid and surface groups.


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Additional Information

J. Y. Li
Affiliation: Institute of Mathematics and Physics, Shijiazhuang Railway Institute, Shijiazhuang 050043, People’s Republic of China
Email: yanjinglee@163.com

J. Wu
Affiliation: Department of Mathematics, National University of Singapore, Block S17 (SOC1), 10, Lower Kent Ridge Road, Republic of Singapore
Email: matwuj@nus.edu.sg

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05339-0
PII: S 0002-9947(2011)05339-0
Keywords: Symmetric commutator subgroup, homotopy group, link group, Brunnian braid, free group, surface group
Received by editor(s): August 4, 2009
Received by editor(s) in revised form: January 25, 2010, and February 28, 2010
Published electronically: February 25, 2011
Additional Notes: The first author was partially supported by the National Natural Science Foundation of China 10971050
The second author was partially supported by the AcRF Tier 1 (WBS No. R-146-000-101-112 and R-146-000-137-112) of MOE of Singapore and a grant (No. 11028104) of NSFC
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.