20.500.12556/RUL-135424 Triangulacije ploskev magistrsko delo Triangulations of surfaces Definicija simplicialnih kompleksov in mnogoterosti nam omogoči razumevanje dveh osnovnih lastnosti ploskev, ki sta Eulerjeva karakteristika in orientabilnost. S pomočjo Dehn-Sommervillovih enačb zapisanih s f- in h-vektorjem definiramo Eulerjevo karakteristiko. Vidimo, da ta, poleg orientabilnosti, natanko določa vse sklenjene ploskve. Do homeomorfizma natančno dobimo eno izmed ploskev: sfero, povezano vsoto n torusov ali povezano vsoto n projektivnih ravnin. Ploskve predstavimo na dva različna načina, s pomočjo mnogokotnika skupaj z njegovo notranjostjo in s pomočjo Heffterjeve prezentacije. Glavna ugotovitev magistrske naloge je minimalna triangulacija ploskev. Oceno za to nam pove Heawoodova domneva, ki je prikazana na primerih sfere, torusa, dvojnega torusa, projektivne ravnine in Kleinove steklenice. The definition of simplicial complex and manifolds allows us to understand two general properties of surfaces, which are Euler characteristic and orientability. Using the Dehn-Sommerville equations written with f- and h-vectors we define the Euler characteristic. We see that this, in addition to orientability, leads us to classification theorem of surfaces. Up to a homeomorphism we get one of the surfaces: a sphere, a connected sum of n tori or a connected sum of n projective planes. We present the surfaces in two different ways: with polygon and with Heffter presentation. The main finding in this thesis is the minimal triangulation of surfaces. We show Heawood conjecture on examples of the sphere, torus, double torus, projective plane and Klein bottle. simplicialni kompleks Eulerjeva karakteristika orientabilnost ploskev minimalne triangulacije simplicial complex Euler characteristic orientability of surfaces minimal triangulations true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2022-03-13 08:15:01 2022-03-13 08:15:08 2024-05-29 12:27:10 0000-00-00 00:00:00 2022 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 515.1 123067 100846083 4345.pdf 4345.pdf 1 D900D38BA6B289E79787C586588CA908 791aa68952073f725e6da40551936f400b754c45b16e9d8b6fdeddb99a0cc174 4f8fcb01-a29d-11ec-8556-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=154489 Fakulteta za matematiko in fiziko 0 0 0