Graf, Christian. Têteàtête : graphs and twists. 2015, Doctoral Thesis, University of Basel, Faculty of Science.

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Official URL: http://edoc.unibas.ch/diss/DissB_11286
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Abstract
This is a PhD thesis in the mathematical field of lowdimensional topology.
Its main purpose is to examine socalled têteàtête twists, which were defined by A'Campo. Têteàtête twists give an easy combinatorial description of certain mapping classes on surfaces with boundary. Whereas the wellknown Dehn twists are twists around a simple closed curve, têteàtête twists are twists around a graph.
It is shown that têteàtête 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 têteàtête 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.
Its main purpose is to examine socalled têteàtête twists, which were defined by A'Campo. Têteàtête twists give an easy combinatorial description of certain mapping classes on surfaces with boundary. Whereas the wellknown Dehn twists are twists around a simple closed curve, têteàtête twists are twists around a graph.
It is shown that têteàtête 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 têteàtête 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 Subtype:  Doctoral Thesis 
Thesis no:  11286 
Thesis status:  Complete 
Number of Pages:  93 p. 
Language:  English 
Identification Number: 

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Last Modified:  23 Feb 2018 13:59 
Deposited On:  21 Jul 2015 15:08 
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