Cusp Volumes of Alternating Knots on Surfaces
Brandon Bavier (MSU)
Abstract: We study the geometry of hyperbolic knots that admit
alternating projections on embedded surfaces in closed 3-manifolds. By
examining certain essential spanning surfaces, we show that, under
mild hypothesis, their cusp area admits two sided bounds in terms of
the twist number of the alternating projection and the genus of the
projection surface. As a result, we derive diagrammatic estimates of
slope lengths and give applications to Dehn surgery. These generalize
results of Lackenby and Purcell about alternating knots in the
3-sphere.