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 will be succeeded by [MTH.B408 : Advanced topics in Geometry D].
Students are expected to
・understand the definitions of mapping class groups, Dehn twists, and braid groups.
Mapping class groups, simple closed curves, Dehn twists, braid groups, Birman's theorem.
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||Practical and/or problem-solving skills|
Standard lecture course
|Course schedule||Required learning|
|Class 1||Manifolds and isotopies||Details will be provided in class.|
|Class 2||Connected sums and handle decompositions||Details will be provided in class.|
|Class 3||Construction and classification of surfaces||Details will be provided in class.|
|Class 4||Mapping class groups of surfaces||Details will be provided in class.|
|Class 5||The Dehn-Nielsen-Baer theorem||Details will be provided in class.|
|Class 6||Curves on surfaces and Dehn twists||Details will be provided in class .|
|Class 7||Braid groups and Birman's theorem||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] and [Topology].