On a relation between the $\mathrm {K}$-cowaist and the $\hat {\mathsf {A}}$-cowaist

Abstract:

The $\mathrm {K}$-cowaist $\mathrm{K-cw}_2(M)$ and the $\hat {\mathsf {A}}$-cowaist $\hat {\mathrm{A}}-\mathrm{cw}_2(M)$ are two interesting invariants on a manifold $M$, which are closely related to the existence of the positive scalar curvature metric on $M$. In this note, we give a detailed proof of the following inequality due to Gromov: $\mathrm{K-cw}_2(M) \le c \hat {\mathrm{A}}-\mathrm{cw}_2(M)$, where $c$ is a dimensional constant.