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

Authors

  • Xiaochun Rong

DOI:

https://doi.org/10.4208/jms.v57n3.24.07

Keywords:

Positive sectional curvature, fundamental groups, the $c(n)$-cyclic conjecture.

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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Published

2024-10-31

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Issue

Vol. 57 No. 3 (2024)

Section

Articles

How to Cite

Fundamental Groups of Manifolds of Positive Sectional Curvature and Bounded Covering Geometry. (2024). Journal of Mathematical Study, 57(3), 358-372. https://doi.org/10.4208/jms.v57n3.24.07