In this thesis, the results of Cattabriga-Gabrovsek regarding the equivalence of links in 3-manifolds will be extended to include genus two 3-manifolds, Dunwoody and Takahashi manifolds. The problem of transitioning from a link's representation via plat closure of a braid to a representation via standard closure of a braid in the cases of S3, handlebodies, and thickened surfaces will be addressed and solved. The solutions to these problems will be accompanied by C++ programs that implement the algorithms described.
Algorithms on braids and links in 3-manifolds / Cavicchioli, P.. - (2023 Jan 17).
Algorithms on braids and links in 3-manifolds
CAVICCHIOLI, PAOLO
2023-01-17
Abstract
In this thesis, the results of Cattabriga-Gabrovsek regarding the equivalence of links in 3-manifolds will be extended to include genus two 3-manifolds, Dunwoody and Takahashi manifolds. The problem of transitioning from a link's representation via plat closure of a braid to a representation via standard closure of a braid in the cases of S3, handlebodies, and thickened surfaces will be addressed and solved. The solutions to these problems will be accompanied by C++ programs that implement the algorithms described.File in questo prodotto:
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Relazione finale Dottorato.pdf
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Tesi_Dottorato_Cavicchioli_Paolo_reviewed.pdf
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