Inanc Baykur: Geometric simple connectivity in dimension four

Title: Geometric simple connectivity in dimension four

Abstract: Every simply connected closed smooth manifold of dimension other than
four admits a handle decomposition without 1-handles; this follows
from the celebrated work of Smale in higher dimensions and of Perelman
in dimension three. Whether the same holds in dimension four remains a
wide open question. I’ll survey the state of the art and explain our
recent (partial) progress, which includes settling a 30-year-old
problem from Kirby’s list.