Estimates of covering type and the number of vertices of minimal triangulationsGovc, Dejan (Avtor) Marzantowicz, Wacław (Avtor) Pavešić, Petar (Avtor) covering typeminimal triangulationLusternik-Schnirelmann categorycup-lengthThe covering type of a space $X$ is a numerical homotopy invariant which in some sense measures the homotopical size of $X$. It was first introduced by Karoubi and Weibel (in Enseign Math 62(3-4):457-474, 2016) as the minimal cardinality of a good cover of a space $Y$ taken among all spaces that are homotopy equivalent to $X$. We give several estimates of the covering type in terms of other homotopy invariants of $X$, most notably the ranks of the homology groups of $X$, the multiplicative structure of the cohomology ring of $X$ and the Lusternik-Schnirelmann category of $X$. In addition, we relate the covering type of a triangulable space to the number of vertices in its minimal triangulations. In this way we derive within a unified framework several estimates of vertex-minimal triangulations which are either new or extensions of results that have been previously obtained by ad hoc combinatorial arguments.20202020-04-18 11:23:42Neznano115223sl