Special Lecture: Michael Yoshizawa (UCSB), 'High Distance Heegaard Splittings via Dehn Twists'

Event Date: 

Thursday, May 2, 2013 - 10:00am to 11:00pm

Event Location: 

  • 4607B South Hall

Event Contact: 

Michael Yoshizawa

Email: myoshi@math.ucsb.edu

Abstract: A Heegaard splitting of a closed 3-manifold is a decomposition of the manifold into two handlebodies of equal genus. The distance of a Heegaard splitting is the path distance in the curve complex between the disk complexes of the two handlebodies and there are known relationships between this distance and the topology of the ambient 3-manifold. In 1987, Andrew Casson and Cameron Gordon proved that Dehn surgery on a certain class of knots in a weakly reducible (distance at most 1) Heegaard surface produces a 3-manifold admitting a strongly irreducible (distance at least 2) Heegaard splitting. I will discuss a generalization of their work that provides upper and lower bounds on the distance of Heegaard splittings obtained by Dehn surgery on knots lying in a Heegaard surface of arbitrary distance.