Autumn Semester 2020 takes place in a mixed form of online and classroom teaching.
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401-4206-17L  Group Actions on Trees

SemesterSpring Semester 2017
LecturersN. Lazarovich
Periodicitynon-recurring course
Language of instructionEnglish



Catalogue data

AbstractAs a main theme, we will explain how an action of a group on a tree enables us to break the group into smaller pieces, and thus gain better understanding of its structure. After introducing the general theory, we will cover various topics in this general theme.
ObjectiveIntroduction to the general theory of group actions on trees, also known as Bass-Serre theory, and various important results on decompositions of groups.
ContentDepending on time we will cover some of the following topics.
- Free groups and their subgroups.
- The general theory of actions on trees, i.e, Bass-Serre theory.
- Trees as 1-dimensional buildings.
- Stallings' theorem.
- Grushko's and Dunwoody's accessibility results.
- Actions on R-trees and the Rips machine.
LiteratureJ.-P. Serre, Trees. (Translated from the French by John Stillwell). Springer-Verlag, 1980. ISBN 3-540-10103-9

C. T. C. Wall. The geometry of abstract groups and their splittings. Revista Matemática Complutense vol. 16(2003), no. 1, pp. 5-101
Prerequisites / NoticeFamiliarity with the basics of fundamental group (and covering theory).

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits4 credits
ExaminersN. Lazarovich
Typesession examination
Language of examinationEnglish
RepetitionThe performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examinationoral 20 minutes
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

No public learning materials available.
Only public learning materials are listed.

Courses

NumberTitleHoursLecturers
401-4206-17 VGroup Actions on Trees
starts in the second week of the semester
2 hrs
Tue15-17HG D 3.2 »
02.05.17-18HG D 5.2 »
16.05.17-18HG D 5.2 »
N. Lazarovich

Groups

No information on groups available.

Restrictions

There are no additional restrictions for the registration.

Offered in

ProgrammeSectionType
Mathematics BachelorSelection: GeometryWInformation
Mathematics MasterSelection: GeometryWInformation