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.
・ understand basics of ordearble groups
・ learn various topics on orderable groups and topology so that one can do further research.
orderable groups, low-dimensional topology, one-dimensional dynamics
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
This is a standard lecture course. There will be some assignments.
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 |
I will give some refereces during the lectures.
I will give some refereces during the lectures.
Assignments (100%).
Not in particular
Not in particular