Topology Seminar: Keegan Boyle

I will discuss how to see symmetries of an alternating knot from any reduced alternating diagram. As a consequence we will see that the quotient of an alternating periodic knot is alternating, and that any alternating knot which is p and q periodic for odd primes p and q is also p*q periodic (c.f. the trefoil which is 2 and 3 but not 6 periodic). The main tool for this is the study of flypes, but we will also mention an approach using spanning surfaces.