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.
aspherical. deficiency. geometric dimension. L^2-homology. knot.
AMS Subject Classification (1991)
Secondary: 57N13, 57Q45
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