Concerning a Bound Problem in Knot Theory
Open Access
- 1 August 1971
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 158 (2) , 423-436
- https://doi.org/10.2307/1995914
Abstract
In a recent paper Treybig shows that if two knot functions determine equivalent knots, then are the ends of a simple sequence of knot functions. In an effort to bound the length of in terms of and (1) a bound is found for the moves necessary in moving one polyhedral disk onto another in the interior of a tetrahedron and (2) it is shown that two polygonal knots in regular position can ``essentially'' be embedded as part of the -skeleton of a triangulation of a tetrahedron, where (1) all 3 cells which are unions of elements of can be shelled and (2) the number of elements in is determined by . A number of ``counting'' lemmas are proved.Keywords
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