Odd Order Group Actions on Alternating Knots
Geometric Topology
2019-06-12 v1
Abstract
Let K be a an alternating prime knot in the 3-sphere. We investigate the category of flypes between reduced alternating diagrams for K. As a consequence, we show that any odd prime order action on K is isotopic through maps of pairs to a single flype. This implies that for any odd prime order action on K there is either a reduced alternating periodic diagram or a reduced alternating free periodic diagram. Finally, we deduce that the quotient of an odd periodic alternating knot is also alternating.
Keywords
Cite
@article{arxiv.1906.04308,
title = {Odd Order Group Actions on Alternating Knots},
author = {Keegan Boyle},
journal= {arXiv preprint arXiv:1906.04308},
year = {2019}
}