Combinatorial Group Theory Seminar
Topology Reading Seminar
Description
The plan is to learn topics and tools of interest to the Low Dimensional Topology group, but we open the invitation to the entire CIMAT community that wants to join. In this semester we will be reading topics on Combinatory Group Theory, we will pay special attention to its relationship with Low Dimensional Topology.
The proposed topics are: -Generators and Relations -Geometric Methods -Free Products and HNN Extensions -Small Cancellation Theory
Time and place
Room G004, Tuesdays from 3:30 to 5:00 PM.
Calendar
This is the calendar in which each of the attendees will be presenting the topics from the Lyndon’s and Schup’s book.
| Date | Theme | Exhibitor | Notes |
|---|---|---|---|
| 29/Aug | II.2 Finite Presentations of Groups | Enrique | We saw the definition of Presentation of groups and Tietze’s Moves Theorem |
| 05/Sep | II.3(1) Calculation of Fox | Jesus | It did not give us time to finish the section, we will continued the next session. |
| 12/Sep | Free week, we go to IPPICTA | ||
| 19/Sep | II.3(2) Connections with Cohomology of the Fox Calculus | Jesus | We saw a brief introduction to Group Cohomology and started with the Reidemeister-Schreier Method |
| 26/Sep | II.4 The Reidemeister-Schreier method | Sebastian | We saw how the Reidemeister-Schreier method allows us to build a presentation of a subgroup |
| 03/Oct | Session suspended due to sick speaker | ||
| 10/Oct | II.5,6 Groups with a single relationship and Magnus treatment | Liceaga | —— |
| 17/Oct | III.1,2 Complexes and covering mappings | Araceli | —— |
| 24/Oct | III.3 Cayley complexes | Juan Parra | —— |
| 31/Oct | III.3 Planar Cayley complexes | Teresa | —— |
Bibliography
- Roger C. Lyndon’s Combinatorial Group Theory, Paul E. Schupp. You can see the book at https://link.springer.com/book/10.1007/978-3-642-61896-3
Other references we are considering are:
- Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations. Wilhelm Magnus, Abraham Karrass, Donald Solitar
- Classical Topology and Combinatorial Group Theory by John Stillwell.