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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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An approach to the polygonal knot problem using projections and isotopies
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by L. B. Treybig PDF
Trans. Amer. Math. Soc. 158 (1971), 409-421 Request permission

Abstract:

The author extends earlier work of Tait, Gauss, Nagy, and Penney in defining and developing properties of (1) the boundary collection of a knot function, and (2) simple sequences of knot functions or boundary collections. The main results are (1) if two knot functions have isomorphic boundary collections then the knots they determine are equivalent, and (2) if two knot functions determine equivalent knots, then the given functions (their boundary collections) are the ends of a simple sequence of knot functions (boundary collections). Matrices are also defined for knot functions.
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 158 (1971), 409-421
  • MSC: Primary 55.20
  • DOI: https://doi.org/10.1090/S0002-9947-1971-0279800-3
  • MathSciNet review: 0279800