Fundamental Groups of Manifolds of Positive Sectional Curvature and Bounded Covering Geometry
Cited by
Export citation
- BibTex
- RIS
- TXT
@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
Copy to clipboard