Nonpositive curvature of complements of real subspace arrangements
by
Richard Scott
Santa Clara University
Coauthors: M. Davis, T. Januszkiewicz

Let V be a finite dimensional real vector space, and let H be the set of hyperplanes in a simplicial hyperplane arrangement in V. We will show that if E is a union of intersections of hyperplanes in H, then the complement V-E is homotopy equivalent to a certain piecewise-Euclidean (cubical) complex which, under appropriate conditions, is nonpositively curved (hence, V-E is a K(, 1)-space). In particular, if H is the reflection arrangement for a Coxeter group W and E is a W-stable codimension-2 union of subspaces, then V-E is a K(, 1)-space.

Date received: April 18, 1998

Copyright © 1998 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # cabb-29.