Combinatorial Group Theory Seminar

Topology Reading Seminar


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.


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 ——


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.
Jesús Rodríguez Viorato
Research Professor

Resarcher Professor with specialized in Low Dimensional Topology