TEORIA GEOMETRICA DEI GRUPPI
Algebra I, Geometria I.
A presentation of 20 minutes on an application of Bass-Serre theory previously discussed with the lecturer, and an oral examination on the content of the course.
The main scope of the course is to introduce the concepts necessary for formulating and understanding the so-called Bass-Serre theory for groups acting on trees. The first step will be to introduce a notion of “graphs” suitable for using geometric concepts like “connectivity”.
Graphs, paths, connectivity, trees; actions of groups on graphs, Cayley graphs; free groups, free products and amalgams, HNN-extensions; quotient graphs, graphs of groups, the fundamental group of a graph of groups, the fundamental theorem for groups acting on trees.
graphs, paths, connection, trees.
group actions on graphs, Cayley graphs;
free groups, free products (with amalgamation), HNN-extensions.
quotient graphs, graph of groups; the fundamental group of a graph of groups; the main theorem of Bass-Serre the
J-P. Serre: Trees, Springer-Verlag, Berlin, 1980.
J. Meier: Groups, Graphs and Trees, London Mathematical Society, Student Texts, 73, CUP, 2008.
O. Bogopolski: Introduction to Group Theory, EMS Textbooks in Mathematics, 2008
Lessons 8 CFU (ECTS).