Establishing isomorphism between tame prime knots in E³

David Emroy Penney, II

Vol. 40 (1972), No. 3, 675–680

DOI: 10.2140/pjm.1972.40.675

Abstract

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 x⁻¹), 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

Milestones

Received: 5 October 1970

Published: 1 March 1972