Geometric Group Theory II (Geometrische Gruppentheorie II)

Geometric Group Theory II

 

Dates:

• Lecture: Monday, 14-16 (c.t.) in SR 10 (Building E 2.4) and Wednesday, 12-14 (c.t.) up to finitely many exceptions.
• Exercise Session: The time for the exercise session will be discussed in the first lecture.

The Team:

• Lecturer: Prof. Dr. Gabriela Weitze-Schmithüsen (weitze [at] math.uni-sb.de)
• Assistant: Pascal Kattler (kattler [at] math.uni-sb.de)

Prerequisites:

Geometric Group Theory (recommended).

Topic:

In Geometric Group Theory II we will see how geometric properties of a group and its Cayley graph, respectively, relate to algebraic properties of the group. One beautiful example of this is the Theorem of Stallings about the ends of Caley graphs of finitely generated groups. An important geometric property of groups is to be 'hyperbolic' which is defined by looking at how 'thin' geodesic triangels are.  It implies several 'good' algebraic properties, among them that the word problem is solvable.

We will furthermore look at particular groups which play a particular role in geometry, as mapping class groups of surfaces and Veech groups.

 

Exams:

The exams will be oral.

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Literature:

• Pierre de la Harpe: Topics in Geometric Group Theory, Chicago Lectures in Mathematics 2003

• Clara Löh: Geometric Group Theory, Springer-Verlag 2017

• John G. Ratcliffe: Foundations of Hyperbolic Manifolds, Springer-Verlag 2019 (https://link.springer.com/book/10.1007/978-3-030-31597-9)

 

Link zum Semesterapparat: https://www.infomath-bib.de/tmp/vorlesungen/mathe-core_geometric-group-theory2.html

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