Problem (ne)evklidskih okolic pri lepljenju 3-mnogoterosti

V tem delu je opisano lepljenje mnogokotnikov vzdolž njihovih robov in utemeljen zaključek, da vedno dobimo ploskev. Ob predpostavki orientabilnosti ploskve je ta ploskev tudi določena. Predstavljen je problem evklidskih okolic oglišč pri analognem lepljenju lic oktaedra, če se evklidske okolice zlepijo v stožec nad ploskvijo pozitivnega rodu.

The problem of (non)-euclidean neighbourhoods obtained by gluing 3-manifolds

This work describes gluing polygons along their edges and concludes that we always obtain a surface. Assuming orientability of the surface, this surface is determined. Presented is the problem of Euclidean neighbourhoods of vertices obtained by analogous gluing of octahedron faces in the case that Euclidean neighbourhoods are glued into a cone of a surface of positive genus.