Document Type
Article
Publication Date
3-15-2012
Publication Title
Topology and Its Applications
Abstract
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.
Repository Citation
Oprea, John and Strom, Jeff, "On Foxʼs M-Dimensional Category and Theorems of Bochner Type" (2012). Mathematics and Statistics Faculty Publications. 209.
https://engagedscholarship.csuohio.edu/scimath_facpub/209
DOI
10.1016/j.topol.2012.01.007
Version
Postprint
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Volume
159
Issue
5
