# Crossing changes and circular Heegaard splittings

Algebra/Geometry/Topology Seminar

#### by Alexander Coward

Institution: University of Sydney
Date: Fri 26th October 2012
Time: 3:15 PM
Location: 213 Richard Berry

Abstract: Twenty years ago Scharlemann and Thompson used deep results from sutured manifold theory to prove that a genus reducing crossing change on a knot maybe be realized as untwisting a Hopf band plumbed onto a minimal genus Seifert surface. This gives a hint that understanding genus reducing crossing changes is closely related to understanding how a compact surface in $$S^3$$ changes when it is twisted. In this talk we use modern technology from the theory of Heegaard splittings to show that understanding when two surfaces are related by a single twist implies the existence of an algorithm to determine when two (hyperbolic or fibered) knots of different genus are related by a single crossing change.