  Let M be a closed 3-manifold which can be triangulated with N simplices. We
prove that any map from M to a genus 2 surface has Hopf invariant at most C^N.
Let X be a closed oriented hyperbolic 3-manifold with injectivity radius less
than epsilon at one point. If there is a degree non-zero map from M to X, then
we prove that epsilon is at least C^{-N}.
