Width, Largeness and Index Theory

  title={Width, Largeness and Index Theory},
  author={Rudolf Zeidler},
  journal={arXiv: Differential Geometry},
  • Rudolf Zeidler
  • Published 2020
  • Mathematics, Physics
  • arXiv: Differential Geometry
In this note, we review some recent developments related to metric aspect of scalar curvature from the point of view of index theory for Dirac operators. In particular, we revisit index-theoretic approaches to a conjecture of Gromov on the width of Riemannian bands $M \times [-1,1]$, and on a conjecture of Rosenberg and Stolz on the non-exstistence of complete positive scalar curvature metrics on $M \times \mathbb{R}$. We show that there is a more general geometric statement underlying both of… Expand
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