Simetrije ploskev

Hrib, Ivo (author), Strle, Sašo (mentor)

V tej diplomski nalogi preučujemo simetrije topoloških ploskev, pri čemer se osredotočamo na orientabilne ploskve in njihovo algebraično strukturo. Raziskujemo, kako se simetrije manifestirajo skozi homeomorfizme in kako lahko z algebraičnimi metodami opišemo njihove lastnosti. Poseben poudarek je namenjen p-simetrijam, ki predstavljajo periodične simetrije reda p. Dokazujemo pogoje za njihov obstoj in preučujemo povezavo med rodom ploskev ter možnimi simetrijami.

• Language: Slovenian
• Keywords: simetrija, ploskve, topologija, homeomorfizmi
• Work type: Bachelor thesis/paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FRI - Faculty of Computer and Information Science
• Year: 2025
• PID: 20.500.12556/RUL-168510
• COBISS.SI-ID: 234537987
• Publication date in RUL: 16.04.2025

Secondary language

• Language: English
• Title: Symmetries of surfaces

Abstract

This thesis explores the symmetries of topological surfaces, focusing on orientable surfaces and their algebraic structure. We investigate how symmetries manifest through homeomorphisms and how algebraic methods can describe their properties. Special attention is given to p-symmetries, which represent periodic symmetries of order p. We establish conditions for their existence and examine the relationship between surface genus and possible symmetries.

• Keywords: symmetry, surfaces, topology, homeomorphisms