A remark on Λ²-enlargeable manifolds

In this paper, we consider the case where the condition “constant near infinity” in the definition of Λ²-enlargeable manifolds is replaced by the condition “locally constant near infinity” and prove that a Λ²-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.