2019 Advanced courses in Geometry C

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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.B333
Credits
1
Academic year
2019
Offered quarter
3Q
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 will be succeeded by [ZUA.B334 : Advanced courses in Geometry D].

Student learning outcomes

Students are expected to
・understand the definitions of mapping class groups, Dehn twists, and braid groups.

Keywords

Mapping class groups, simple closed curves, Dehn twists, braid groups, Birman's theorem.

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 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

Textbook(s)

None 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.B334 : Advanced courses in Geometry D

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

Students are expected to have passed [Geometry I], [Geometry II] and [Topology].

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