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.

The seminar is virtual via Zoom. If you are interested in participating, please contact Stephan Stadler (stadler

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