Mathematics Colloquia and Seminars
Uniqueness in Waldhausen’s theorem (joint with M. Freedman)Geometry/Topology
|Speaker:||Martin Scharlemann, UCSB|
|Start time:||Tue, Mar 13 2018, 1:10PM|
It is a famous theorem of Waldhausen that any genus g Heegaard splitting surface H in S3 is isotopic to the standard genus g splitting surface H0. Rieck’s modern account of Waldhausen's theorem exploits a theorem of Casson and Gordon on weakly reducible Heegaard splittings. They show that a weak reduction of the splitting leads to a way of breaking up the surface into a connected sum of lower genus splittings, at which point induction can be used.
But how unique is the isotopy of H to H0? To what extent is the isotopy determined by the choice of a weak reduction? We discuss this in the context of a conjecture of Powell about isotopies of H0 to itself.