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On Knots and DNA
Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska fakulteten.
2017 (engelsk)Independent thesis Basic level (degree of Bachelor), 10,5 poäng / 16 hpOppgave
Abstract [en]

Knot theory is the mathematical study of knots. In this thesis we study knots and one of its applications in DNA. Knot theory sits in the mathematical field of topology and naturally this is where the work begins. Topological concepts such as topological spaces, homeomorphisms, and homology are considered. Thereafter knot theory, and in particular, knot theoretical invariants are examined, aiming to provide insights into why it is difficult to answer the question "How can we tell knots appart?". In knot theory invariants such as the bracket polynomial, the Jones polynomial and tricolorability are considered as well as other helpful results like Seifert surfaces. Lastly knot theory is applied to DNA, where it will shed light on how certain enzymes interact with the genome.

sted, utgiver, år, opplag, sider
2017. , s. 58
Emneord [en]
Knot theory, Topology, Homology, Jones polynomial, Bracket polynomial, Tangles, DNA
HSV kategori
Identifikatorer
URN: urn:nbn:se:liu:diva-144294ISRN: LiTH-MAT-EX--2017/17--SEOAI: oai:DiVA.org:liu-144294DiVA, id: diva2:1185932
Fag / kurs
Mathematics
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Examiner
Tilgjengelig fra: 2018-04-04 Laget: 2018-02-26 Sist oppdatert: 2018-04-04bibliografisk kontrollert

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