Please use this identifier to cite or link to this item: https://doi.org/10.1090/S0002-9947-2011-05339-0
Title: On symmetric commutator subgroups, braids, links and homotopy groups
Authors: Li, J.Y.
Wu, J. 
Keywords: Brunnian braid
Free group
Homotopy group
Link group
Surface group
Symmetric commutator subgroup
Issue Date: Jul-2011
Citation: Li, J.Y., Wu, J. (2011-07). On symmetric commutator subgroups, braids, links and homotopy groups. Transactions of the American Mathematical Society 363 (7) : 3829-3852. ScholarBank@NUS Repository. https://doi.org/10.1090/S0002-9947-2011-05339-0
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. © 2011 American Mathematical Society.
Source Title: Transactions of the American Mathematical Society
URI: http://scholarbank.nus.edu.sg/handle/10635/103763
ISSN: 00029947
DOI: 10.1090/S0002-9947-2011-05339-0
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