Siegel der Universität Augsburg

Universität Augsburg
Institut für Mathematik

Siegel der Universität Augsburg

 

Seminar Topics in Symplectic Geometry

 

Frau Jana Nickel
Universität Cambridge

 
spricht am
 
Montag, 23. Juli 2018
 
um
 
10:00 Uhr
 
im
 
Raum 2004 (L1)
 
über das Thema:
 

»Complexes of Curves and Mapping Class Groups«

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



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