Trent Schirmer will speak tomorrow, Thur Jan 29, on:
GK-Trisections of 4-manifolds and the Poincare Conjecture
Abstract: A GK-trisection of a 4-manifold X is a decomposition of X into
three simple handlebodies that intersect in a nice way. Introduced by Gay
and Kirby, this construction bears many similarities to Heegaard splittings
of 3-manifolds, and is amenable to study using 3-manifold techniques, as is
well illustrated in a recent paper by Meier and Zupan. In my talk I will
describe how GK-trisections provide new approaches to the 4-dimensional
smooth Poincare Conjecture. These approaches are essentially the analogues
of failed "Heegaard splitting" approaches to the 3-dimensional Poincare
Conjecture. However, the fact that the 3d Poincare conjecture is true
implies several statements about or related to Heegaard splittings that
maybe, just maybe, can somehow be lifted to statements about trisections
that imply the 4-d conjecture.
