Whitehead Doubles of Arborescent Knots.
Topology Seminar,
Rice University, Houston, TX, January 2008


Abstract
Canonical genus is frequently hard to compute. In the case of Whitehead doubles of knots, Tripp conjectured that the canonical genus is equal to the crossing number of the original knot. This has previously been shown to be true for torus knots (Tripp) and 2-bridge knots (Nakamura). We will extend this result to arborescent knots and, more generally, to knots with certain underlying polyhedra.