COVERING HOMOTOPY 3-SPHERES

We prove the following theorem: for any closed orientable 3-manifold M and any homotopy 3-sphere SIGMA, there exists a simple 3-fold branched covering p:M --> SIGMA. We also propose the conjecture that, for any primitive branched covering p:M --> N between orientable 3-manifolds, g(M) greater-than-or-equal-to g(N), where g denotes the Heegaard genus. By the above mentioned result, the genus 0 case of such conjecture is equivalent to the Poincare conjecture.