## Course## Geometric Group Theory## Winter term 21/22## Prof. Dr. Linus Kramer## with Dr. Amandine Escalier |

*Geometric Group Theory 2*is planned.

The course is aimed at students in or past their 5th semester in mathematics (BSc or MSc).
It can be used as part of a specialization in *Algebra*, *Topology*, or *Geometric Structures*
- contact me if you have questions about this.

The planned **topics** of the course include group actions,
free groups, free products, Hopfian groups, residually finite groups,
amalgams, HNN extensions, presentations,
fundamental groups, covering spaces, the Seifert-Van Kampen Theorem, and subgroups
of free groups.

**Prerequisites** include the material from the basic courses
in analysis and algebra, and some point-set topology.

The class takes place Monday and Thursday 8 - 10 in lecture hall M4. It starts on
Monday, Oct 11 at 8:15.
As long as the university permits this, the classes will be in-person.
The 4 lectures Dec 13 - 23 can be found as videos in the
Learnweb.
There you will also find additional material.
In January the class will be given in a hybrid format (in person and as a zoom live stream).

The course is given in English.

We have weekly exercise sessions. Solving the exercises and participating in the exercise sessions is a vital part of the course. The exercise sessions take place on Monday afternoon in lecture hall M6, 16:00 - 18:00 or via zoom, depending on the pandemic situation. You may hand in your solutions in letterbox 162 or send them by email to Leon Pernak.

We will have oral exams in February for this course. The exact dates have yet to be fixed.

#### Literature (you will find these books in the math library):

- Magnus, Karras, Solitar, Combinatorial group theory
- Camps, Rebel, Rosenberger, Einführung in die kombinatorische und geometrische Gruppentheorie
- Lyndon, Schupp, Combinatorial group theory
- Robinson, A course in the theory of groups
- Geoghegan, Topological methods in group theory
- de la Harpe, Topics in geometric group theory
- Bogopolski, Introduction to group theory
- Stallings, Topology of finite graphs
- Fine, Rosenberger, Wienke, Topics in infinite group theory
- MacLane, Categories for the working mathematician
- Spanier, Algebraic topology
- Hatcher, Algebraic topology

#### Exercise problems:

In Exercise 4 we need that*g*Exercise 3.2 had to be changed.

_{i}∈G_{i}\CExercise sheet | from | hand in by | |
---|---|---|---|

Sheet 1 | 14.10.2021 | 21.10.2021 | |

Sheet 2 | 21.10.2021 | 28.10.2021 | |

Sheet 3 | 28.10.2021 | 04.11.2021 | |

Sheet 4 | 04.11.2021 | 11.11.2021 | |

Sheet 5 | 11.11.2021 | 18.11.2021 | |

Sheet 6 | 18.11.2021 | 25.11.2021 | |

Sheet 7 | 25.11.2021 | 02.12.2021 | |

Sheet 8 | 02.12.2021 | 09.12.2021 | There was a typo in Exercise 3 |

Sheet 9 | 09.12.2021 | 16.12.2021 | |

Sheet 10 | 16.12.2021 | 23.12.2021 | |

Sheet 11 | 03.01.2021 | 13.01.2022 | |

Sheet 12 | 13.01.2022 | 20.01.2022 |

Hand in your solution in letter box 162 or by email to Leon Pernak.

#### Class notes:

These are my handwritten notes for class. If you spot mistakes or if you have question, please contact me.

Intro |

Chapter 1 |

Chapter 2 |

Chapter 3 |

Chapter 4 |

Chapter 5 |

Chapter 6 |

Chapter 7 |