Ploskve v ${\mathbb R}^4$

Marinić, Alan (author), Strle, Sašo (mentor)

V diplomskem delu obravnavamo načine za opis in konstrukcijo zavozlanih ploskev, vloženih v $4$-razsežen prostor. Navedemo dve različni metodi za obravnavo ploskev v ${\mathbb R}^4$ ter dokažemo ekvivalenco med njima. Poleg tega definiramo še dve konstrukciji, ki iz vozlov pridelajo zavozlane ploskve.

• Language: Slovenian
• Keywords: zavozlana ploskev, filmska predstavitev, zlomljena ploskev, vozel
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2024
• PID: 20.500.12556/RUL-162760
• UDC: 515.1
• COBISS.SI-ID: 209449987
• Publication date in RUL: 27.09.2024

Secondary language

• Language: English
• Title: Surfaces in ${\mathbb R}^4$

Abstract

In this thesis we show methods for description and construction of knotted surfaces embedded in the $4$-space. We study two different descriptions of knotted surfaces and prove equivalence between them. In addition, we study constructions that generate knotted surfaces from given knots.

• Keywords: knotted surface, movie picture, broken surface diagram, knot