Xiaochung Rong
Rutgers University
Partial rigidity of nonpositively curved manifolds
Abstract: Let $M$ be closed $n$-manifold of negative sectional curvature. A classical result of Preismann states that any abelian subgroup of the fundamental group is cyclic. By bringing in the discrete group technique, Margulis showed that if rescaling the metric so that the curvaure between $-1$ and $0$, then there exists at least one point at which the injectivity radius is bounded below by a constant $\epsilon(n)>0$. In this talk, we discuss results that describes the special circumstances under which the conclusions of the Preismann and Margulis theorem can fail.