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Publishing Language: Chinese | Open Access

Fundamental groups of manifolds of positive sectional curvature

School of Mathematical Sciences, Capital Normal University, Beijing 100048
Mathematics Department, Rutgers University New Brunswick, State of New Jersey 08903
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Abstract

Let M be a compact n-manifold of positive sectional curvature. We will review classical results on the fundamental group of M, a motivation on the c ( n ) -cyclic conjecture that the fundamental group of M contains a cyclic subgroup of index bounded above by c ( n ) , a constant depending only on n, and we will survey partial results (up to date) on the c ( n ) -cyclic conjecture.

Keywords

positive sectional curvatureconjecture on almost cyclic fundamental groupsequivariant Gromov-Hausdorff convergenceAlexandrov geometry
CLC number: O186.1 Document code: A

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Journal of Capital Normal University (Natural Science Edition)
Volume 47 Issue 1,
February 2026
Pages 1-13
DOI: 10.19789/j.1004-9398.2026.01.001

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Cite this article:
RONG X. Fundamental groups of manifolds of positive sectional curvature. Journal of Capital Normal University (Natural Science Edition), 2026, 47(1): 1-13. https://doi.org/10.19789/j.1004-9398.2026.01.001

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Received: 04 August 2024
Published: 01 February 2026
© The editorial department of Journal of Capital Normal University (Natural Science Edition) 2024.

This is an open access article under the CC BY-NC-ND 4.0 license (https://creativecommons.org/licenses/by-nc-nd/4.0/).