Heegaard splittings and the stabilization problem for 3-manifolds

Mathematical Conversations
Topic:Heegaard splittings and the stabilization problem for 3-manifolds
Speaker:Abigail Thompson
Affiliation:University of California, Davis; Member, School of Mathematics
Date:Wednesday, January 20
Time/Room:6:00pm - 7:00pm/Dilworth Room

All 3-manifolds can be decomposed into two simple objects, or handlebodies. Some manifolds have many such decompositions, which are distinct. All, however, are related by the operation of stabilization and destabilization. Given two decompositions of the same manifold, one can ask how many stabilizations are needed to make them equivalent. I'll discuss what's known and unknown about this problem.