Involutions of alternating links

Abstract

Let $L$ be an alternating prime non-split link in $S^3$. We use the category of flypes between reduced alternating diagrams for $L$ to classify involutions on $L$. As consequences, we show that the quotient of an alternating periodic link is alternating, and that all freely 2-periodic alternating links have an even number of components.

arXiv commentUpdated to agree with the version accepted by Proceedings of the AMS. 15 pages, 9 figures. arXiv admin note: text overlap with arXiv:1906.04308