Remark: 335-01. An integral scalar curvature bound for real simplicial volume

Authors: OpenAI. Family 335.

Title: An integral scalar curvature bound for real simplicial volume.

Abstract: We prove the integral scalar-curvature inequality proposed by Gromov. For every dimension n ≥ 3, there is a constant $a_n{}gt 0$, depending only on n, such that ${}displaystyle {}int_M({}mathop{{}mathrm{Scal}}{}nolimits _g{}-){}{n/2}{},dV_g{}ge a_n{}|M{}|$ for every closed connected oriented smooth n-manifold M and every smooth Riemannian metric g. Here ${}mathop{{}mathrm{Scal}}{}nolimits _g{}-:={}max{}{0,-{}mathop{{}mathrm{Scal}}{}nolimits _g{}}$, and ${}|M{}|$ is real simplicial volume. The proof uses the nonnegative-scalar-curvature vanishing theorem of the companion paper on rational inessentiality.

This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.