On CAT(0) structures for free-by-cyclic groups

We construct CAT(0) spaces on which various free-by-cyclic groups act. Let G be the free-by-cyclic group F(a,c1,…,cn,d)⋊φZ with φ determined by ϕ(a)=a, ϕ(cj)=cjaκ, and ϕ(d)=dw, where w is some word not containing d. Our main result is that if the exponent sum of cn in w is non-zero, then there is a CAT(0) metric space on which G acts properly discontinuously and cocompactly by isometries.