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Group cohomology SemesterWiSe 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
MV, MArGeo, MGAGeo ECTS 4,5 |