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SemesterapparatWritten on 24.10.23 by Christian Steinhart Dear students, we now have a "Semesterapparat" in the library, that is you can find suitable and supplemental lecture under the link "Semesterapparat". If you are more interested in the topological point of view, I highly recommend the book from Farb&Margalit (we basically start there at Chapter… Read more Dear students, we now have a "Semesterapparat" in the library, that is you can find suitable and supplemental lecture under the link "Semesterapparat". If you are more interested in the topological point of view, I highly recommend the book from Farb&Margalit (we basically start there at Chapter 2). Hubbard and Imayoshi&Taniguchi give a more analytical and quite thorough introduction to Teichmüller space and some examples. In Hubbard you also find some exercises suitable for the lecture ;-) In Ahlfors you find the more classical (also analytical) approach, but we will mostly follow the first three books. Yours, Christian |
Deformation Spaces
We will discuss Teichmüller space as a typical example of deformation spaces.
Content:
We will introduce Teichmüller space and its geometry. We will roughly follow Chapter 2 and part of Chapter 3 of Benson Farb and Dan Margalits book "A Primer on Mapping Class Groups". Topics will include:
- Mapping class group
- Fenchel-Nielsen Coordinates
- Teichmüller metric
- Thurston metric
- Foliations
- (Thurston'S Classification of elements of the mapping class group)
Dates:
Lecture: Tuesdays 8:30-10 am in SR 9
Exam: There will be the possibility for an oral exam at the end of the course for students.
Lecturer: Dr. Christian Steinhart
- algebra
- basic knowledge in topology
- complex analysis
Literature:
- Semesterapparat
- Farb-Margalit: "A Primer on Mapping Class Groups"
- Imayoshi-Taniguchi: "An Introduction to Teichmüller Spaces"
- Hubbard: "Teichmüller Theory and Applications to Geometry, Topology, and Dynamics"