Rank gradients of infinite cyclic covers of 3-manifolds

Abstract

Given a 3-manifold M with no spherical boundary components, and a primitive class ϕin H^1(M;Z), we show that the following are equivalent: (1) ϕis a fibered class, (2) the rank gradient of (M,ϕ) is zero, (3) the Heegaard gradient of (M,ϕ) is zero.

17 pages, minor updates and modifications, to be published by the Mich Math J