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Tête-à-tête : graphs and twists

Graf, Christian. Tête-à-tête : graphs and twists. 2015, PhD Thesis, University of Basel, Faculty of Science.

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Official URL: http://edoc.unibas.ch/diss/DissB_11286

Abstract

This is a PhD thesis in the mathematical field of low-dimensional topology.
Its main purpose is to examine so-called tête-à-tête twists, which were defined by A'Campo. Tête-à-tête twists give an easy combinatorial description of certain mapping classes on surfaces with boundary. Whereas the well-known Dehn twists are twists around a simple closed curve, tête-à-tête twists are twists around a graph.
It is shown that tête-à-tête twists describe all the (freely) periodic mapping classes. This leads, among other things, to a stronger version of Wiman's 4g+2 theorem from 1895 for surfaces with boundary.
We also see for some tête-à-tête twists how they can be used to generate the mapping class group of closed surfaces.
Another main result is a simple criterion to decide whether a Seifert surface of a link is a fibre surface. This gives a short topological proof of the fact that a Murasugi sum is fibred if and only if its two summands are.
Advisors:A'Campo, Norbert
Committee Members:Boileau, Michel and Oancea, Alexandru
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Ehemalige Einheiten Mathematik & Informatik > Geometrie (A'Campo)
Item Type:Thesis
Thesis no:11286
Bibsysno:Link to catalogue
Number of Pages:93 p.
Language:English
Identification Number:
Last Modified:30 Jun 2016 10:58
Deposited On:21 Jul 2015 15:08

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