Tête-à-tête graphs and twists
|Director of thesis||Norbert A'Campo|
|Co-director of thesis|
|Summary of thesis||
The main purpose of my thesis is to examine so-called tête-à-tête twists. Those were defined by A'Campo and 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.
On closed surfaces, some tête-à-tête twists can be used to generate the mapping class group.
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 is fibred if and only if its two summands are.
|Administrative delay for the defence||2014|