A remark on $\Lambda^2$-enlargeable manifolds

In this note, we consider the case where the condition ``constant near infinity" in the definition of $\Lambda^2$-enlargeable manifolds is replaced by the condition ``locally constant near infinity" and prove that a $\Lambda^2$-enlargeable manifold in this modified sense still cannot carry a complete Riemannian metric of positive scalar curvature. As a consequence, we give another proof of Wang-Zhang's theorem on the generalized Geroch conjecture for complete spin manifolds.