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- W2947604443 abstract "This paper is devoted to prove the existence of $q$-periodic alternating projections of prime alternating $q$-periodic knots. The main tool is the Menasco-Thistlethwaite's Flyping theorem. Let $K$ be an oriented prime alternating knot that is $q$-periodic with $qgeq 3$, i.e. $K$ admits a symmetry that is a rotation of order $q$. Then $K$ has an alternating $q$-periodic projection. As applications, we obtain the crossing number of a $q$ -periodic alternating knot with $qgeq 3$ is a multiple of $q$ and we give an elementary proof that the knot $12_{a634} $ is not 3-periodic; this proof does not depend on computer computations as in Periodic knots and Heegaard Floer correction terms by Stanilav Jabuka and Swatee Naik (arXiv:1307.5116 [math.GT])." @default.
- W2947604443 created "2019-06-07" @default.
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- W2947604443 date "2019-05-31" @default.
- W2947604443 modified "2023-09-27" @default.
- W2947604443 title "Periodic projections of alternating knots" @default.
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