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Macroscopic band width inequalities

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Speaker: 
Daniel Räde
Affiliation: 
Universität Augsburg
Date: 
Thu, 2021-01-14 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.

 

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

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