Corrigendum to: “Aspherical four-manifolds and the centres of two-knot groups”

Abstract

out that the proof of the key Lemma on "hopfian" rings in w of [1] is incorrect.As I have been unable to find a correct argument, the results on pages 465-469 are moot.(Corollaries 2 and 3 on page 470 are true as it is easy to see that the lemma holds for any commutative ring, while the results in w use only Kaplansky's original theorem, and not the lemma.)I hope that some ring-theorist may be able to prove the lemma.In the first line of page 469, the map from /-/~(C*) to Homr (H2(C,I, F) given by the universal coefficient spectral sequence is, a priori, only a monomorphism.However the theorem is still true (without any essential change in the argument), modulo the lemma.A. Suciu has pointed out that the map 9 in line 1 of page 471 should be replaced by its square 4 2, to ensure that the mapping torus M be orientable.I am grateful to Dyer and Suciu for their observations.

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