We show that Lissajous knots are equivalent to billiard knots in a cube. We consider also knots in general 3-dimensional billiard tables. We analyse symmetry of knots in billiard tables and show in particular that the Alexander polynomial of a Lissajous knot is a square modulo 2.
@article{bwmeta1.element.bwnjournal-article-bcpv42i1p145bwm,
author = {Jones, Vaughan and Przytycki, J\'ozef},
title = {Lissajous knots and billiard knots},
journal = {Banach Center Publications},
volume = {43},
year = {1998},
pages = {145-163},
zbl = {0901.57012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv42i1p145bwm}
}
Jones, Vaughan; Przytycki, Józef. Lissajous knots and billiard knots. Banach Center Publications, Tome 43 (1998) pp. 145-163. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv42i1p145bwm/
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