Invariants of piecewise-linear knots

Volume 42 / 1998

Richard Randell Banach Center Publications 42 (1998), 307-319 DOI: 10.4064/-42-1-307-319


We study numerical and polynomial invariants of piecewise-linear knots, with the goal of better understanding the space of all knots and links. For knots with small numbers of edges we are able to find limits on polynomial or Vassiliev invariants sufficient to determine an exact list of realizable knots. We thus obtain the minimal edge number for all knots with six or fewer crossings. For example, the only knot requiring exactly seven edges is the figure-8 knot.


  • Richard Randell

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