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.|
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].