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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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On symmetric commutator subgroups, braids, links and homotopy groups
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by J. Y. Li and J. Wu PDF
Trans. Amer. Math. Soc. 363 (2011), 3829-3852 Request permission


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:
  • J. Wu
  • Affiliation: Department of Mathematics, National University of Singapore, Block S17 (SOC1), 10, Lower Kent Ridge Road, Republic of Singapore
  • Email:
  • 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
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 363 (2011), 3829-3852
  • MSC (2010): Primary 55Q40, 20F12; Secondary 20F36, 57M25
  • DOI:
  • MathSciNet review: 2775829