19067
Lecture
WiSe 13/14: Surfaces and Automorphisms
Holger Reich, Fabian Lenhardt
Comments
One can always equip a compact orientable differentiable surface S with the structure of a one-dimensional complex manifold. Alternatively one can equip it with a metric. In fact with the exception of the torus and the sphere every such surface S admits a hyperbolic metric, i.e. a metric of constant curvature -1.
In this lecture we want to study these additional structures on surfaces. How many complex structures/hyperbolic structures are there on a given surface? This question leads to the definition of Teichmüller space and the moduli space of complex/hyperbolic structures.
The mapping class group is the group of orientation preserving self-diffeomorphism, where two self-diffeomorphism are identified if they can be connected by a path of self-diffeomorphisms. The mapping class group acts on Teichmüller space and is an important tool to study this group.
No advanced algebraic topology, Riemannian geometry or Riemann surface theory is assumed. All concepts will be developed in the lecture. However we do assume familiarity with the basic notions from topology, analysis and group theory and some mathematical experience. close
In this lecture we want to study these additional structures on surfaces. How many complex structures/hyperbolic structures are there on a given surface? This question leads to the definition of Teichmüller space and the moduli space of complex/hyperbolic structures.
The mapping class group is the group of orientation preserving self-diffeomorphism, where two self-diffeomorphism are identified if they can be connected by a path of self-diffeomorphisms. The mapping class group acts on Teichmüller space and is an important tool to study this group.
No advanced algebraic topology, Riemannian geometry or Riemann surface theory is assumed. All concepts will be developed in the lecture. However we do assume familiarity with the basic notions from topology, analysis and group theory and some mathematical experience. close
32 Class schedule
Regular appointments
Tue, 2013-10-15 10:00 - 12:00
Tue, 2013-10-22 10:00 - 12:00
Tue, 2013-10-29 10:00 - 12:00
Tue, 2013-11-05 10:00 - 12:00
Tue, 2013-11-12 10:00 - 12:00
Tue, 2013-11-19 10:00 - 12:00
Tue, 2013-11-26 10:00 - 12:00
Tue, 2013-12-03 10:00 - 12:00
Tue, 2013-12-10 10:00 - 12:00
Tue, 2013-12-17 10:00 - 12:00
Tue, 2014-01-07 10:00 - 12:00
Tue, 2014-01-14 10:00 - 12:00
Tue, 2014-01-21 10:00 - 12:00
Tue, 2014-01-28 10:00 - 12:00
Tue, 2014-02-04 10:00 - 12:00
Tue, 2014-02-11 10:00 - 12:00
Wed, 2013-10-16 10:00 - 12:00
Wed, 2013-10-23 10:00 - 12:00
Wed, 2013-10-30 10:00 - 12:00
Wed, 2013-11-06 10:00 - 12:00
Wed, 2013-11-13 10:00 - 12:00
Wed, 2013-11-20 10:00 - 12:00
Wed, 2013-11-27 10:00 - 12:00
Wed, 2013-12-04 10:00 - 12:00
Wed, 2013-12-11 10:00 - 12:00
Wed, 2013-12-18 10:00 - 12:00
Wed, 2014-01-08 10:00 - 12:00
Wed, 2014-01-15 10:00 - 12:00
Wed, 2014-01-22 10:00 - 12:00
Wed, 2014-01-29 10:00 - 12:00
Wed, 2014-02-05 10:00 - 12:00
Wed, 2014-02-12 10:00 - 12:00