OnL 2-homology and asphericity

Abstract

We useL 2 methods to show that if a group with a presentation of deficiency one is an extension ofZ by a finitely generated normal subgroup then the 2-complex corresponding to any presentation of optimal deficiency is aspherical and to prove a converse of the Cheeger-Gromov-Gottlieb theorem relating Euler characteristic and asphericity. These results are applied to the Whitehead conjecture, 4-manifolds and 2-knot groups.