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- Academic unit or major
- Mathematics
- Instructor(s)
- Nosaka Takefumi Ito Tetsuya
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Intensive ()
- Group
- -
- Course number
- ZUA.E334
- Credits
- 2
- Academic year
- 2018
- Offered quarter
- 4Q
- Syllabus updated
- 2018/8/20
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
An orderable group is a group with total ordering which is invariant under the group action itself. Although this definition is purely algebraic, it is related to one-dimensional dynamics and low-dimensional topology, and recently orderable groups are actively studied in various point of view.
In this lecture we will explain various aspects of orderable groups including dynamics, topology, and combinatorics, and give a lecture on fundamental aspects and recent developments. Here I will emphasize a connection to low-dimensional topology.
Student learning outcomes
・ understand basics of ordearble groups
・ learn various topics on orderable groups and topology so that one can do further research.
Keywords
orderable groups, low-dimensional topology, one-dimensional dynamics
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
Class flow
This is a standard lecture course. There will be some assignments.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | I will give a lecture for the following topics: ・ Algebraic basics of orderable groups ・ Orderable groups and one-dimensional dynamics ・ Space of orderings and isolated orderings ・ orderings on the fundamental group of 3-manifolds, foliations, and Heegaard Floer homology ・ bi-invariant orderings and Alexander invariants | to be specified in each lecture |
Textbook(s)
I will give some refereces during the lectures.
Reference books, course materials, etc.
I will give some refereces during the lectures.
Assessment criteria and methods
Assignments (100%).
Related courses
- MTH.E646 ： Special lectures on current topics in Mathematics Q
- MTH.E434 ： Special lectures on advanced topics in Mathematics D
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Not in particular
Other
Not in particular
