Prime Decomposition of Knots in Lorenz-like Templates

Details Prime Decomposition of Knots in Lorenz-like Templates Prime Decomposition of Knots in Lorenz-like Templates

2003-08-08

arxiv.org/abs/math/0308085v1

J. Knot Theory Ramifications 2 (1993), no. 4, 453--462

Mathematics

Dynamical Systems

10 pages; 9 figures, many with multiple parts

Scientific paper

R. F. Williams showed that all knots in the Lorenz template are prime. His proof included the cases where any number of positive twists were added to one of the template's branches. However, Williams does give an example of a composite knot in a template with a single negative twist. Below we will show that in all the negative cases composite knots do exist, and give a mechanism for producing many examples.

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