Ryffel, Levi Salomon (2024). Twisting braids and surfaces. (Thesis). Universität Bern, Bern

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Abstract

This thesis covers two twisting notions, namely that of Dehn twists and that of Fox’s twist moves. More precisely, in the first part we characterise closed embedded discs in surfaces that are bounded by a circuit curve system in terms of a particular relation called the cycle relation between the associated Dehn twists. We also characterise bouquets of curves in a similar vein. In the process, we classify all circuits of curves in terms of whether the corresponding Dehn twists generate an Artin group. In the second part we relate Przytycky’s obstructions on the HOMFLY polynomial for two links to be related by twist moves to the crossing number and the braid index. We also estimate the cobordism distance between connected sum powers of trefoil or hexafoil links and three strand torus links.

Item Type:	Thesis
Dissertation Type:	Single
Date of Defense:	12 February 2024
Subjects:	500 Science > 510 Mathematics
Institute / Center:	08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics
Depositing User:	Hammer Igor
Date Deposited:	04 Mar 2024 15:34
Last Modified:	04 Mar 2024 15:34
URI:	https://boristheses.unibe.ch/id/eprint/4920

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