2019 Advanced courses in Geometry D

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Academic unit or major
Mathematics
Instructor(s)
Endo Hisaaki 
Course component(s)
Lecture
Day/Period(Room No.)
Mon3-4(H115)  
Group
-
Course number
ZUA.B334
Credits
1
Academic year
2019
Offered quarter
4Q
Syllabus updated
2019/3/18
Lecture notes updated
-
Language used
English
Access Index

Course description and aims

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 [ZUA.B333 : Advanced courses in Geometry C].

Student learning outcomes

Students are expected to
・understand proofs of fundamental theorems on mapping class groups.

Keywords

The Dehn-Lickorish theorem, Lickorish-Humphries generators, Torelli groups, Johnson homomorphisms.

Competencies that will be developed

Intercultural skills Communication skills Specialist skills Critical thinking skills Practical and/or problem-solving skills
- - - -

Class flow

Standard lecture course

Course schedule/Required learning

  Course schedule Required learning
Class 1 Properties of Dehn twists Details will be provided during each class session
Class 2 Lickorish generators Details will be provided during each class session
Class 3 The Dehn-Lickorish theorem (1) Details will be provided during each class session
Class 4 The Dehn-Lickorish theorem (2) Details will be provided during each class session
Class 5 Finite presentations of mapping class groups Details will be provided during each class session
Class 6 Siegel modular groups and Torelli groups Details will be provided during each class session
Class 7 Johnson homomorphisms Details will be provided during each class session
Class 8 Evaluation of progress Details will be provided during each class session

Textbook(s)

Non required

Reference books, course materials, etc.

B. Farb and D. Margalit, A Primer on Mapping Class Groups, Princeton University Press.

Assessment criteria and methods

Exams and reports. Details will be provided during class sessions.

Related courses

  • MTH.B301 : Geometry I
  • MTH.B302 : Geometry II
  • ZUA.B301 : Geometry I
  • MTH.B341 : Topology
  • ZUA.B333 : Advanced courses in Geometry C

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students are expected to have passed [Geometry I], [Geometry II], [Topology] and [Advanced courses in Geometry C].

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