53 research outputs found
A new criterion for knots with free periods
Let and an integer. A knot in the three-sphere is
said to be a -lens knot if and only if it covers a link in the lens
space . In this paper, we use the second coefficient of the HOMFLY
polynomial to provide a necessary condition for a knot to be a -lens
knot. As an application, it is shown that this criterion rules out the
possibility of being -lens for 80 among the 84 knots with less than 9
crossings.Comment: 14 pages, 1 figur
Skein Algebras of the solid torus and symmetric spatial graphs
We use the topological invariant of spatial graphs introduced by S. Yamada to
find necessary conditions for a spatial graph to be periodic with a prime
period. The proof of the main result is based on computing the Yamada skein
algebra of the solid torus then proving that this algebra injects into the
Kauffman bracket skein algebra of the solid torus.Comment: 13 pages, 7 figure
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