|Coordinates:||JH Michell Theatre in the Richard Berry Building|
|Speaker:||Abigail Thompson (University of California, Davis)|
|Title:||3-manifolds with distance two Heegaard splittings|
(Joint work with Hyam Rubinstein.)
Casson and Gordon showed that irreducible 3-manifolds with distance one Heegaard splittings are Haken. We consider 3-manifolds with distance two Heegaard splittings. These are well-understood in the case of genus two. When the genus is greater than two, we show they fall into a few groups, one of which is Haken manifolds. Another is those that can be constructed by gluing three handlebodies together (carefully) along their boundaries. Under some constraints we are able to show that the fundamental groups of the handlebodies inject into the fundamental group of the manifold.