Topologija za krojače (ali kako ploskev razrezati na hlače)

slovenian

2026

volume 13, issue 2

cuttings of surfaces   decompositions of surfaces   multigraph   orientable surfaces   pants decompositions   sphere with three holes

Univerza v Ljubljani, Fakulteta za matematiko in fiziko
(Obvezni izvod spletne publikacije)

In this article, it will be shown how some orientable surfaces can be cut into components, homeomorphic to a sphere with three holes (also known as a pair of pants). Cuttings of surfaces will be discussed. Cut systems will have a crucial role here. Cut systems tell us how to cut the surface. Then the decompositions of surfaces will be considered. Those are sets of components into which the cut system cuts our surface. A surface, known as pants, will be presented next. Those are surfaces homeomorphic to a sphere with three holes. Then, the focus will be shifted to a special type of decomposition, namely pants decompositions. Those are decompositions, where every component is homeomorphic to a pair of pants. It will be shown for which orientable surfaces pants decompositions exist. Then, a method for assigning a multigraph to a pants decomposition will be presented. Conversely, it will be shown how a pants decomposition can be “encoded” with a multigraph. Then the moves will be presented. Those are ways to move between different pants decompositions of the given surface. In the end, two essential results that ensure the well-definedness of moves will be proven, i.e., the moves always give us a new pants decomposition.

23.09.2026