Enlargeable length-structure and scalar curvatures

Jialong Deng Mathematisches Institut, Georg-August-Universität, Göttingen, Germany

Differential Geometry Metric Geometry mathscidoc:2206.10005

Annals of Global Analysis and Geometry, 60, 217-230, 2021.5
We define enlargeable length-structures on closed topological manifolds and then show that the connected sum of a closed n-manifold with an enlargeable Riemannian length-structure with an arbitrary closed smooth manifold carries no Riemannian metrics with positive scalar curvature. We show that closed smooth manifolds with a locally CAT(0)-metric which is strongly equivalent to a Riemannian metric are examples of closed manifolds with an enlargeable Riemannian length-structure. Moreover, the result is correct in arbitrary dimensions based on the main result of a recent paper by Schoen and Yau. We define the positive MV-scalar curvature on closed orientable topological manifolds and show the compactly enlargeable length-structures are the obstructions of its existence.
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@inproceedings{jialong2021enlargeable,
  title={Enlargeable length-structure and scalar curvatures},
  author={Jialong Deng},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220621162657049534421},
  booktitle={Annals of Global Analysis and Geometry},
  volume={60},
  pages={217-230},
  year={2021},
}
Jialong Deng. Enlargeable length-structure and scalar curvatures. 2021. Vol. 60. In Annals of Global Analysis and Geometry. pp.217-230. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220621162657049534421.
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