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 [ZUA.B334 : Advanced courses 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 during each class session |
Class 2 | Connected sums and handle decompositions | Details will be provided during each class session |
Class 3 | Construction and classification of surfaces | Details will be provided during each class session |
Class 4 | Mapping class groups of surfaces | Details will be provided during each class session |
Class 5 | The Dehn-Nielsen-Baer theorem | Details will be provided during each class session |
Class 6 | Curves on surfaces and Dehn twists | Details will be provided during each class session |
Class 7 | Braid groups and Birman's theorem | Details will be provided during each class session |
Class 8 | Evaluation of progress | Details will be provided during each class session |
None required
B. Farb and D. Margalit, A Primer on Mapping Class Groups, Princeton University Press.
Exams and reports. Details will be provided during class sessions.
Students are expected to have passed [Geometry I], [Geometry II] and [Topology].