2021/08/22 by Dejan Govc, Govc, Dejan, Wacław Marzantowicz +3
Mathematics · #57Q15 #57R05 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 55M #Secondary 55M30
paper · pdf · doi:10.48550/arxiv.2108.09853
openalex publication_date 2021/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a recent publication (D. Govc, W. Marzantowicz, P. Pavesic, Estimates of covering type and the number of vertices of minimal triangulations, Discr. Comp. Geom. 63 (2019), 31-48) we have introduced a new method, based on the Lusternik-Schnirelmann category and the cohomology ring of a space X, that yields lower bounds for the size of a triangulation of X. In this paper we present an important extension that takes into account the fundamental group of X. In fact, if it contains elements of finite order, then one can often find cohomology classes of high 'category weight', which in turn allow for much stronger estimates of the size of triangulations of X. We develop several weighted estimates and then apply our method to compute explicit lower bounds for the size of triangulations of orbit spaces of cyclic group actions on a variety of spaces including products of spheres, Stiefel manifolds, Lie groups and highly-connected manifolds.