Jiayin Pan University of California, Santa Cruz
Nonnegative Ricci curvature and virtual abelianness in dimensions less than 12
Wednesday, October 7 · 4:00 PM · McHenry 4130
Abstract
For any complete Riemannian manifold \(M^n\) with nonnegative Ricci curvature and sublinear diameter growth, we establish a dimensional constraint \(n\ge 4s(s-1)+k+1\) if the fundamental group \(\pi_1(M)\) contains a torsion-free nilpotent subgroup of rank \(k\) and step \(s\ge 2\). As a consequence, if such a manifold \(M\) has dimension \(n<12\), then \(\pi_1(M)\) is almost abelian. This is a joint work with Dimitri Navarro and Xingyu Zhu.