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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Petal Diagrams and Seifert Surfaces

Gardiner, Jason Robert 02 August 2021 (has links)
Petal diagrams of knots are projections of knots to the plane such that the diagram has exactly one crossing. Petal diagrams offer a convenient and combinatorial way of representing knots via their associated petal permutation. In this thesis we study the fundamental group and Seifert surfaces of knots in petal form. Using the Seifert-Van Kampen theorem, we give a group presentation of the fundamental group of the knot complement of a knot in petal form. We then discuss Seifert surfaces and use decomposition diagrams to represent the Seifert surfaces of knots in petal form. We finally give an algorithm to produce a set of decomposition diagrams for a spanning surface of a knot in petal form and prove that for incompressible surfaces such decomposition diagrams are unique up to perturbation moves.

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