Isotropic curvature, macroscopic dimension Filling radius of contractible loops and fundamental group

Friday, October 18, 2013 -
3:00pm to 4:00pm
I will discuss the proof of a conjecture of Gromov's to the effect that manifolds with uniformly positive isotropic curvature (and bounded geometry) are macroscopically 1-dimensional on the scale of the isotropic curvature. One of the main techniques involved is modeled on Donaldson's version of H\"ormander technique to produce (almost) holomorphic sections. We use this to produce  sections of the restriction of the complexified tangent bundle of M to a stable embedded minimal disk which destabilize the disk if the distance grows too much. As a consequence we prove that compact manifolds with positive isotropic curvature have virtually free fundamental groups.
Speaker: 
Gabriele La Nave
University of Illinois, Urbana-Champaign
Event Location: 
Fine Hall 314