Mrežna homologija vozlov

Šipec, Katarina (author), Strle, Sašo (mentor)

V tem delu opišemo tri vrste mrežne homologije vozlov -- popolnoma blokirano, neblokirano in enostavno blokirano homologijo. Predstavljene so povezave z nekaterimi drugimi vozelnimi invariantami, natančneje s Seifertovimi ploskvami, rodom vozla, Alexandrovim polinomom in razvozlavnim številom.

• Language: Slovenian
• Keywords: vozel, homologija, mrežna homologija, invarianta, mrežni diagram, dvojno stopničenje, Alexandrov polinom, razvozlavno število, Seifertova ploskev, rod
• Work type: Master's thesis/paper
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2023
• PID: 20.500.12556/RUL-153325
• COBISS.SI-ID: 178295043
• Publication date in RUL: 22.12.2023

Secondary language

• Language: English
• Title: Grid homology for knots

Abstract

We describe three types of grid homology for knots -- fully blocked, unblocked and simply blocked homology. Connections to some other knot invariants are presented, in particular to Seifert surfaces, the knot genus, the Alexander polynomial and the unknotting number.

• Keywords: knot, homology, grid homology, invariant, grid diagram, bigrading, Alexander polynomial, unknotting number, Seifert surface, genus