Triangulations with few vertices of manifolds with non-free fundamental group
Pavešić, Petar
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. Posbej, 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.
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