Abstract:In his book "Metric structures for Riemannian and non-Riemannian spaces", Gromov defined two properties of Riemannian manifolds, ellipticity and quasiregular ellipticity, and suggested that there may be a connection between the two. Since then, groups of researchers working independently have proved strikingly similar results about these two concepts. We obtain new topological obstructions to the two properties: most notably, we show that closed manifolds of both types must have virtually abelian fundamental group. We also give the first examples of open manifolds which are elliptic but not quasireguarly elliptic and vice versa. Whether there is a direct connection between these properties -- and, in particular, whether they are equivalent for closed manifolds -- remains elusive.
From: Fedor Manin [view email]
[v1]
Thu, 24 Oct 2024 19:47:36 UTC (36 KB)
[v2]
Sun, 22 Dec 2024 20:32:08 UTC (37 KB)
[v3]
Thu, 4 Dec 2025 05:03:17 UTC (41 KB)
[v4]
Mon, 1 Jun 2026 21:28:01 UTC (45 KB)
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