Abstract
This is a PhD thesis in the mathematical field of low-dimensional topology. Its main purpose is to examine so-called tete-a-tete twists, which were defined by A'Campo. Tete-a-tete 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, tete-a-tete twists are twists around a graph. It is shown that tete-a-tete 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 tete-a-tete 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.
Published Version
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