2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/223219Let 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}.17 pages. In the first version of the paper, there was a mistake on page 6 in the proof of Lemma 1. The paper is corrected, and some parts have been simplifiedDifferential Geometry53C23, 57M50text