Universität Regensburg   IMPRESSUM   DATENSCHUTZ
Fakultät für Mathematik Universität Regensburg
Group cohomology
Semester
WiSe 2023 / 24

Lecturer
Kevin Li

Type of course (Veranstaltungsart)
Vorlesung

German title
Kohomologie von Gruppen

Contents
Group cohomology is an invariant that connects algebraic and geometric properties of groups in
several ways. For example, group cohomology admits descriptions in terms of homological algebra and
also in terms of topology. Group cohomology naturally comes up in algebra, topology, and geometry.
For example, group cohomology allows to - generalise the Hilbert 90 theorem in Galois theory, -
classify group extensions with given Abelian kernel, - generalise the classical group-theoretic
transfer, - generalise finiteness properties of groups (such as finiteness, finite generation,
finite presentability, ...), - study which finite groups admit free actions on spheres, - ...

Literature
Brown's book ``Cohomology of groups", Löh's lecture notes from SS19.

Recommended previous knowledge
Basic group theory, basic algebraic topology (CW-complexes, fundamental group, homology), basic
homological algebra (projective modules, Ext, Tor). We can recall some of these prerequisits during
the first exercise class.

Time/Date
Friday 8-10

Location
M 104

Additional question session
Time/Date: Thursday 8-10, roughly every second week, (no meeting on 19.10.23)
Location: M 009

Course homepage
tba
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration
  • Registration for course work/examination/ECTS: FlexNow
Course work (Studienleistungen)
  • Oral examination (without grade): Duration: 30 min, Date: tba
Examination (Prüfungsleistungen)
  • Oral exam: Duration: 30 min, Date: tba, re-exam: Date: tba
Modules
MV, MArGeo, MGAGeo

ECTS
4,5