Topological surfaces were classified at the end of the 19th century. However the study of their automorphisms (the so-called mapping class group) is important in many modern branches of mathematics including dynamics, topology and geometry. The work of William Thurston revolutionised the study of surface automorphisms by positing a classification in terms of dynamical properties in ground breaking work described in his famous Bulletin Article. The objective of this seminar is to explore Thurston's theory starting with the basics of hyperbolic geometry as well as describing important examples illustrating the theory. The picture above shows what happens to a curve under a so-called taffy puller.

A. Casson and S. Bleiler, Automorphisms of Surfaces after Nielsen and Thurston, LMS

B. Farb and D. Margalit, A primer on mapping class groups, Princeton Univ. Press

A. Fathi, F. Laudenbach and V. Poenaru, Thurston’s Work on Surfaces, Princteon University Press

W. Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bulletin of AMS

• Organisational meeting/distribution of topics: Mo 5 February at 16:00-17:00 in M201 (NOTE:
  Change of time place!!!)
• Registration for course work/examination/ECTS: FlexNow

• Detailed written report of the seminar talk