Hamilton's injectivity radius estimate for sequences with almost   nonnegative curvature operators
  We give a new and complete proof of Hamilton's injectivity radius estimate for sequences with bounded and almost nonnegative curvature operators, unbounded diameters, and bump-like origins. Such sequences arise in particular from dilations about a singularity of the Ricci flow on a 3-manifold. 
Bennett Chow, Dan Knopf, and Peng Lu