Groups, Geometry, and Dynamics

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GGD summary

Volume 1, Issue 3, 2007, pp. 301–309

DOI: 10.4171/GGD/14

The ℓ²-cohomology of hyperplane complements

Michael W. Davis (1), Tadeusz Januszkiewicz (2) and Ian J. Leary (3)

(1) Department of Mathematics, Ohio State University, 231 W 18th Avenue, OH 43210, COLUMBUS, UNITED STATES
(2) Department of Mathematics, Ohio State University, 231 W 18th Avenue, OH 43210-1174, COLUMBUS, UNITED STATES
(3) Department of Mathematics, Ohio State University, 231 W 18th Avenue, OH 43210, COLUMBUS, UNITED STATES

We compute the ℓ²-Betti numbers of the complement of a finite collection of affine hyperplanes in ℂⁿ. At most one of the ℓ²-Betti numbers is nonzero.

Keywords: Hyperplane arrangements, L²-cohomology.