Coordinates: JH Michell Theatre in the Richard Berry Building
Speaker: Martin Scharlemann (UC Santa Barbara)
Title: New examples of manifolds with multiple genus 2 Heegaard splittings
Abstract: (Joint work with John Berge.)

At the end of the last millenium, Rubinstein and I presented an exhaustive but duplicative list of all closed orientable 3-manifolds that could have more than one genus 2 Heegaard splittings. Recently John Berge found a gap in the argument, via an example which demonstrated that the list was not exhaustive. The gap is now filled, but properties common to the earlier examples are not universally shared by the new examples. For example, some have Hempel distance 3, and for some it is not clear that a single stabilization suffices to make the distinct splittings isotopic. One source of examples is a certain 4-component link L in (S1xS2)#(S1xS2) with the property that generic Dehn surgery on L is a 3-manifold with two inequivalent genus 2 Heegaard splittings, and each of these Heegaard splittings is of Hempel distance exactly 3.
Slides: Scharlemann_Hyamfest.pdf (1.9 MB)