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REPRESENTATIVITY AND NON-CONTRACTIBLE SEPARATING CYCLES OF EMBEDDINGS ON THE TRIPLE TORUS

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datacite.subject.fosNatural sciences::Mathematics
dc.contributor.authorJuwawo, Precious
dc.date.accessioned2025-01-21T06:37:03Z
dc.date.available2025-01-21T06:37:03Z
dc.date.issued2024-05-01
dc.descriptionSubmitted to the Department of Mathematical Sciences, School of Natural and Applied Sciences in (partial) fulfillment of the requirements for the award of the degree of Master of Science in Mathematical Sciences.
dc.description.abstractWe consider Ellingman’s and Zhao’s method of proving that every 4 representative graph embedding on the double torus contains a Non-Contractible Separating Cycle (NSC). They proved this main result by considering critical embeddings; which are embeddings that are very close to having NSCs. We adopt the method in proving an extension of the same theorem to a surface of one genus higher; the triple torus. The method works efficiently in proving our main result that every 4 representative embedding on the triple torus contains two NSCs which separates the triple torus into 3 connected components, namely punctured tori, two of them with one boundary circle and one with two boundary circles. Our results are obtained by employing equivalence of embeddings and homeomorphism of surfaces to Ellingman and Zhao’s method.
dc.identifier.urihttps://dspace.unima.ac.mw/handle/123456789/607
dc.language.isoen
dc.schoolscentersoptionsb0e8094e-c230-4f28-8ae9-b0fc60729932
dc.subjectRepresentativity
dc.subjectNon-contractible separating cycles
dc.subjectTriple torus
dc.subjectEllingman
dc.subjectZhao
dc.subjectHomeomorphism
dc.subjectDouble torus
dc.subjectPunctured tori
dc.supervisorea951455-b2b6-4861-88ca-29374e64b5a0
dc.titleREPRESENTATIVITY AND NON-CONTRACTIBLE SEPARATING CYCLES OF EMBEDDINGS ON THE TRIPLE TORUS
dc.typetext::thesis::master thesis
dspace.entity.typePublication
oairecerif.author.affiliationUniversity of Malawi

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