Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


On the Alexander polynomials of certain three-component links
HTML articles powered by AMS MathViewer

by Mark E. Kidwell PDF
Proc. Amer. Math. Soc. 71 (1978), 351-354 Request permission


Let L be a three-component link all of whose linking numbers are zero. Write the Alexander polynomial of L as $\Delta (x,y,z) = (1 - x)(1 - y)(1 - z)f(x,y,z)$. Then the integer $|f(1,1,1)|$ is a perfect square.
  • E. Artin, Geometric algebra, Interscience Publishers, Inc., New York-London, 1957. MR 0082463
  • Joan S. Birman, Braids, links, and mapping class groups, Annals of Mathematics Studies, No. 82, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1974. MR 0375281
  • R. H. Fox, Some problems in knot theory, Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) Prentice-Hall, Englewood Cliffs, N.J., 1962, pp. 168–176. MR 0140100
  • Fujitsugu Hosokawa, On $\nabla$-polynomials of links, Osaka Math. J. 10 (1958), 273–282. MR 102820
  • Dale Rolfsen, Knots and links, Mathematics Lecture Series, No. 7, Publish or Perish, Inc., Berkeley, Calif., 1976. MR 0515288
  • H. Seifert, Über das Geschlecht von Knoten, Math. Ann. 110 (1935), no. 1, 571–592 (German). MR 1512955, DOI 10.1007/BF01448044
  • Guillermo Torres, On the Alexander polynomial, Ann. of Math. (2) 57 (1953), 57–89. MR 52104, DOI 10.2307/1969726
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 55A25
  • Retrieve articles in all journals with MSC: 55A25
Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 71 (1978), 351-354
  • MSC: Primary 55A25
  • DOI:
  • MathSciNet review: 0482737