A remark on ${\mathrm{\Lambda }}^2$-enlargeable manifolds

In this note, we consider the case where the condition constant near infinity" in the definition of $Λ^2$-enlargeable manifolds is replaced by the condition locally constant near infinity" and prove that a ${\mathrm{\Lambda }}^2$-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.