Surgery up to homotopy equivalence for nonpositively curved manifolds

Let Mn{M^n} be a smooth closed manifold which admits a metric of nonpositive curvature. We show, using a theorem of Farrell and Hsiang, that if n+k⩾6n + k \geqslant 6, then the surgery obstruction map [M×Dk,∂;G/TOP]→Ln+kh(π1M,w1(M))\left [ {M \times {D^k},\partial ;G / {\text {TOP}}} \right ] \to L_{n + k}^h\left ( {{\pi _1}M,{w_1}\left ( M \right )} \right ) is injective, where L∗hL_ * ^h are the obstruction groups for surgery up to homotopy equivalence.