Volume 57, Issue 3
Fundamental Groups of Manifolds of Positive Sectional Curvature and Bounded Covering Geometry

Xiaochun Rong

J. Math. Study, 57 (2024), pp. 358-372.

Published online: 2024-10

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  • 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 $v.$

  • AMS Subject Headings

53C21, 53C23, 53C24

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COPYRIGHT: © Global Science Press

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@Article{JMS-57-358, author = {Rong , Xiaochun}, title = {Fundamental Groups of Manifolds of Positive Sectional Curvature and Bounded Covering Geometry}, journal = {Journal of Mathematical Study}, year = {2024}, volume = {57}, number = {3}, pages = {358--372}, 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 $v.$

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v57n3.24.07}, url = {http://global-sci.org/intro/article_detail/jms/23493.html} }
TY - JOUR T1 - Fundamental Groups of Manifolds of Positive Sectional Curvature and Bounded Covering Geometry AU - Rong , Xiaochun JO - Journal of Mathematical Study VL - 3 SP - 358 EP - 372 PY - 2024 DA - 2024/10 SN - 57 DO - http://doi.org/10.4208/jms.v57n3.24.07 UR - https://global-sci.org/intro/article_detail/jms/23493.html KW - Positive sectional curvature, fundamental groups, the $c(n)$-cyclic conjecture. AB -

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 $v.$

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