# Macroscopic band width inequalities

Posted in
Speaker:
Daniel Räde
Zugehörigkeit:
Universität Augsburg
Datum:
Don, 14/01/2021 - 16:30 - 18:00

Inspired by Gromov's work on 'Metric inequalities with scalar
curvature' we establish band width inequalities for Riemannian bands of
the form $(V=M\times[0,1],g)$, where $M^{n-1}$ is a closed manifold. We
introduce a new class of orientable manifolds we call 'filling
enlargeable' and prove:
If $M$ is filling enlargeable and all unit balls in the universal cover
of $(V,g)$ have volume less than a constant $\frac{1}{2}\epsilon_n$, then $width(V,g)\leq1$.
We show that if a closed orientable manifold is enlargeable or
aspherical then it is filling enlargeable. Furthermore we establish that
whether a closed orientable manifold is filling enlargeable or not only
depends on the image of the fundamental class under the classifying map
of the universal cover.