Vol. 40, No. 3, 1972

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Establishing isomorphism between tame prime knots in E3

David Emroy Penney, II

Vol. 40 (1972), No. 3, 675–680

The “formula” of a polygonal knot in E3 is defined by appropriate labeling of the crossings in the regular projection of the knot. Admissible transformations of such formulas are defined (for example, cancellation of the consecutive symbols x and x1), and prime formulas are defined. It is shown that if two knots have formulas which are equivalent by applications of admissible transformations, and one of the formulas is prime, then the knots are equivalently embedded in E3.

Mathematical Subject Classification
Primary: 55A25
Received: 5 October 1970
Published: 1 March 1972
David Emroy Penney, II