Topology and Its Applications
We show that cat M (X)=Cat (jm),where cat m(X) is Fox’s m-dimensional category, jm:X→X [m] is the mth Postnikov section of X and cat (X) is the Lusternik–Schnirelmann category of X. This characterization is used to give new “Bochner-type” bounds on the rank of the Gottlieb group and the first Betti number for manifolds of non-negative Ricci curvature. Finally, we apply these methods to obtain Bochner-type theorems for manifolds of almost non-negative sectional curvature.
Oprea, John and Strom, Jeff, "On Foxʼs M-Dimensional Category and Theorems of Bochner Type" (2012). Mathematics Faculty Publications. 209.
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