Peter Feller

ETH Zürich


The Dehn twist coefficient and irrational rotation behaviour


Geometry and Topology Seminar


14th November 2023, 2:00 pm – 3:00 pm
Fry Building, 2.04


In this talk, we consider the Dehn twist coefficient (DTC). The DTC is a map from the mapping class group of a surface S with a marked circular boundary component to the reals, i.e. DTC: MCG(S)->R. Intuitively speaking, it measures how much a mapping class twists about the marked boundary component.

Historically (starting with Gabai and Oertel), the DTC has been considered for surfaces of finite type. As a consequence of the Nielson-Thurston classification of surface diffeomorphisms, the DTC takes on rational values on surfaces of finite type. We extend the concept to surfaces of infinite type by means of a new characterization of the DTC that works for all S. We will further provide examples of surfaces for which the DTC takes on all reals. For the latter we will explicitly construct mapping classes of surfaces with DTC a given real number.

A large part of the talk will be hands-on constructions of diffeomorphisms of surfaces (with some input going back to Poincare). The talk will be low tech with a focus on drawing pictures on surfaces.






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