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 - <p style="text-align: justify;">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 $v &gt; 0,$ then
the fundamental group $\pi_1(M)$ has a cyclic subgroup of index bounded above by a
constant depending only on $n$ and $v.$</p>