L^2-Homology and asphericity

Author

Jonathan A. Hillman

Status

Research Report 95-26
3 August 1995

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

Abstract

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

Content

The paper is available in the following forms:

TeX dvi format:: l2-hom-sph.dvi.gz (16kB) or l2-hom-sph.dvi (39kB)
PostScript:: l2-hom-sph.ps.gz (37kB) or l2-hom-sph.ps (123kB)

To minimize network load, please choose the smaller gzipped .gz form if and only if your browser client supports it.

Sydney Mathematics and Statistics