Fundamental Groups of Manifolds of Positive Sectional Curvature and Bounded Covering Geometry

Xiaochun Rong

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Source: Crossref

Published: Oct 31, 2024

DOI: 10.4208/jms.v57n3.24.07

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Source abstract

Let $M$ be an $n$ -manifold of positive sectional curvature $≥ 1.$ In this paper, we show that if the Riemannian universal covering has volume at least $v > 0,$ then the fundamental group $\pi_1(M)$ has a cyclic subgroup of index bounded above by a constant depending only on $n$ and $v.$

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Fundamental Groups of Manifolds of Positive Sectional Curvature and Bounded Covering Geometry — Mathematical Frontier Network