2019/06/10 by Keegan Boyle, Boyle, Keegan
Computer Science · Mathematics · #57M25 #57M27 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1906.04308
openalex publication_date 2019/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.