A homotopy fibration theorem in dimension four

Abstract

We adapt and extend work of Barge to show that, under assumptions on the fundamental group alone, an infinite cyclic cover of a 4-dimensional Poincare duality complex with Euler characteristic 0 satisfies Poincare duality with local coefficients and so is a 3-dimensional Poincaré duality complex. This implies that, modulo the 5-dimensional s -cobordism theorem, each spun fibred classical knot is determined topologically (up to orientation) by its group together with a weight class.