Universität Augsburg
|
Frau Jana Nickel
Universität Cambridge
spricht am
Montag, 23. Juli 2018
um
10:00 Uhr
im
Raum 2004 (L1)
über das Thema:
Abstract: |
This talk about the complex of curves and mapping class group of surfaces is based on my essay “Complexes of Curves”, which I wrote during the master programme Part III Mathematics 2017/2018 at the University of Cambridge and which was supervised by Dr Henry Wilton. The complex of curves of a surface S is an abstract simplicial complex providing information about the intersection patterns of essential simple closed curves in S. It establishes a relation between the combinatorial, topological structure of the manifold S and the algebraic structure of its mapping class group Mod(S). In my talk, we will see that the complex of curves is a crucial tool with regard to the generation of the mapping class group. I aim to present some basic knowledge about the theory of curves, mapping class groups and Dehn twists, to prove that the complex of curves of certain surfaces is path-connected and to expound some other essential concepts concerning the finite generation of Mod(S) by means of Dehn twists and half-twists, such as the Birman Exact Sequence and the pure mapping class group. The chief source of literature I used for my essay is “A Primer on Mapping Class G |
Hierzu ergeht herzliche Einladung. |
Kai Cieliebak |