The aim of this lecture is to familiarize the students with the basic language of
and some fundamental theorems for mapping class groups of surfaces.
This course is a continuation of [MTH.B407 : Advanced topics in Geometry C1].
Students are expected to
・understand proofs of fundamental theorems on mapping class groups.
The Dehn-Lickorish theorem, Lickorish-Humphries generators, Torelli groups, Johnson homomorphisms.
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Standard lecture course
Course schedule | Required learning | |
---|---|---|
Class 1 | Properties of Dehn twists | Details will be provided during in class. |
Class 2 | Lickorish generators | Details will be provided in class. |
Class 3 | The Dehn-Lickorish theorem (1) | Details will be provided in class. |
Class 4 | The Dehn-Lickorish theorem (2) | Details will be provided in class. |
Class 5 | Finite presentations of mapping class groups | Details will be provided in class. |
Class 6 | Siegel modular groups and Torelli groups | Details will be provided in class. |
Class 7 | Johnson homomorphisms | Details will be provided in class. |
Class 8 | Evaluation of progress | Details will be provided in class. |
None required
B. Farb and D. Margalit, A Primer on Mapping Class Groups, Princeton University Press.
Exams and reports. Details will be provided in class.
Students are expected to have passed [Geometry I], [Geometry II], [Topology] and [Advanced topics in Geometry C1].