20.500.12556/RUL-115222 Triangulations with few vertices of manifolds with non-free fundamental group Majhne triangulacije mnogoterosti s fundamentalno grupo, ki ni prosta We study lower bounds for the number of vertices in a PL-triangulation of a given manifold $M$. While most of the previous estimates are based on the dimension and the connectivity of $M$, we show that further information can be extracted by studying the structure of the fundamental group of $M$ and applying techniques from the Lusternik-Schnirelmann category theory. In particular, we prove that every PL-triangulation of a $d$-dimensional manifold ($d\ge 3$) whose fundamental group is not free has at least $3d+1$ vertices. As a corollary, every $d$-dimensional ($\mathbb{Z}_p$-)homology sphere that admits a PL-triangulation with less than $3d$ vertices is homeomorphic to $S^d$. Another important consequence is that every triangulation with small links of $M$ is combinatorial. V članku obravnavamo spodnje meje za število oglišč v PL-triangulacijah dane mnogoterosti $M$. Prej znane ocene uporabljajo dimenzijo in povezanost $M$, mi pa pokažemo, da je mogoče dobiti boljše ocene z uporabo fundamentalne grupe in tehnik Lusternik-Schnirelmannove kategorije. Glavni rezultat je, da je za PL-triangulacijo $d$-razsežne mnogoterosti ($d\ge 3$) katere fundamentalna grupa ni prosta potrebnih vsaj $3d + 1$ oglišč. Posebej, vsaka $d$-razsežna homološka sfera, ki dopušča kombinatorno triangulacijo z manj kot $3d$ oglišč je PL-homeomorfna običajni $d$-sferi. Druga pomembna posledica je, da so vse triangulacije z majhnimi okvirji kombinatorne. minimal triangulation PL-manifold homology sphere good cover Lusternik-Schnirelmann category true false false Angleški jezik Slovenski jezik Neznano 2020-04-18 11:16:09 2020-04-18 11:16:11 2022-08-27 04:00:14 0000-00-00 00:00:00 2019 0 0 Str. 1453-1463 iss. 6 Vol. 149 Dec. 2019 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 515.164 0308-2105 10.1017/prm.2018.136 18671705 26180608 RAZ_Pavesic_Petar_2019.pdf RAZ_Pavesic_Petar_2019.pdf 1 443FAB51612241F72776EDAEC0D14BF6 490378552db1ebe8477887256383b67f3d61f4ec1eec820d32c037beed531cb3 6ecef887-a1b8-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=127921 Fakulteta za matematiko in fiziko 0 0 0