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Nonnegative Ricci curvature, nilpotency, and Hausdorff dimension

By Jiayin Pan

Continuing Wei's presentation, we will talk about how the universal covers of Nabonnand-type examples came to our attention. One geometric feature in these examples is that the minimal representing loops of $\pi_1(M,p)$ must escape from any bounded sets. This leads to wild limit orbits in the asymptotic cones of $\widetilde{M}$: these orbits are not convex and have large Hausdorff dimension. Then we will discuss the relations in general among the above-mentioned escape phenomenon, orbits in the asymptotic cones, and the virtual abelianness / nilpotency of the fundamental groups.

Information about the video

  • Date of recording 29/11/2023
  • Date of publication 15/12/2023
  • Institution IHES
  • Language English
  • Audience Researchers
  • Format MP4

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