Commensurability classes of $(-2,3,n)$ pretzel knot complements

Geometry Topology Seminar
Friday, November 5, 2010 - 11:05am
1 hour (actually 50 minutes)
Skiles 255
California State University, Chico
(joint work with M. Macasieb) Let $K$ be a hyperbolic $(-2, 3, n)$ pretzel knot and $M = S^3 \setminus K$ its complement. For these knots, we verify a conjecture of Reid and Walsh: there are at most three knotcomplements in the commensurability class of $M$. Indeed, if $n \neq 7$, weshow that $M$ is the unique knot complement in its class.