On virtual chirality of 3-manifolds

Abstract

We prove that if a prime 3-manifold $M$ is not finitely covered by the 3-sphere or a product manifold, then $M$ is virtually chiral, that is, it has a finite cover that does not admit an orientation-reversing self-homeomorphism. In general, if a 3-manifold contains a virtually chiral prime summand, then it is virtually chiral.