20.500.12556/RUL-115223 Estimates of covering type and the number of vertices of minimal triangulations Ocene tipa pokritja in števila oglišč v minimalnih triangulacijah The 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. Tip pokritja prostora $X$ je homotopska invarianta, ki v določenem smislu meri homotopsko velikost $X$. Vpeljala sta jo Karoubi in Weibel kot minimalno moč dobrega pokritja prostora $Y$ med vsemi prostori $Y$, ki so homotopsko ekvivalentni $X$. V članku podamo vrsto ocen za tip pokritja s pomočjo drugih homotopskih invariant, med katerimi izstopajo homološke grupe, kohomološki kolobar in Lusternik-Schnirelmannova kategorija. Poleg tega v članku povežemo tip pokritja poliedra s številom oglišč v minimalni triangulaciji. Tako izpeljemo na enovit način vrsto ocen, ki so bodisi nove, bodisi posplošitve ocen, ki so v preteklosti slonele na ad hoc kombinatornih ocenah. covering type minimal triangulation Lusternik-Schnirelmann category cup-length tip pokritja minimalna triangulacija Lusternik-Schnirelmannova kategorija dolžina kohomološkega produkta true false false Angleški jezik Slovenski jezik Neznano 2020-04-18 11:23:42 2020-04-18 11:23:45 2022-08-27 04:00:14 0000-00-00 00:00:00 2020 0 0 Str. 31-48 iss. 1 Vol. 63 Jan. 2020 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 515.14 0179-5376 10.1007/s00454-019-00092-z 18627417 25342208 RAZ_Govc_Dejan_2020.pdf RAZ_Govc_Dejan_2020.pdf 1 9778A3C60E38B8FFFDB1D7934419B5A7 b53b9185e9afc77f4d4ee874349196a67bb0280a364540a31fd5c08b54e472f3 6edd56ba-a1b8-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=127923 Fakulteta za matematiko in fiziko 0 0 0