3/7/2006

Yoav Moriah
Technion

Twisted torus knots and distance one Heegaard splittings

(Joint work with Eric Sedgwick) It may come as a surprise to low dimensional topologists that there is no known example of a 3-manifold with a non-minimal genus Heegaard splitting of distance one. We describe an infinite family of manifolds having Heegaard splittings which are candidates to be distance one. In the process we also reveal why finding such examples is so elusive.