L^2-Homology and asphericity


Jonathan A. Hillman


Research Report 95-26
3 August 1995

Israel Journal of Mathematics 99 (1997), 271-283


We use L^2 methods to show that if a group with a presentation of deficiency one is an extension of Z 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 several open problems on knot groups and on the homotopy types of certain 4-manifolds.

Key phrases

aspherical. deficiency. geometric dimension. L^2-homology. knot.

AMS Subject Classification (1991)

Primary: 57M05
Secondary: 57N13, 57Q45


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