IMPRESSUM    DATENSCHUTZ
	Fakultät für Mathematik	Universität Regensburg
Group Cohomology Semester SoSe 2019 Lecturer Clara Löh Type of course (Veranstaltungsart) Vorlesung 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. Different choices of coefficients for group cohomology leads to different invariance properties, whence to different types of applications. 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, ...), characterise the class of amenable groups (which are important in large-scale geometry), study which finite groups admit free actions on spheres, characterise which groups admit non-trivial quasi-morphisms, prove that certain groups admit significantly different dynamical systems, prove rigidity results in topology and geometry ... In this course, we will introduce the basics of group homology and cohomology, starting with elementary descriptions and calculations. Depending on the background of the audience, we will then either focus on a more algebraic perspective or on a more topological one. Recommended previous knowledge All participants should have a firm background in Analysis I/II (in particular, basic point set topology, e.g., as in Analysis II in WS 2011/12), in Linear Algebra I/II, and basic knowledge in group theory (as covered in the lectures on Algebra). Knowledge about manifolds as in Analysis IV is not necessary, but helpful. Knowledge about basic homological algebra (as in the last two weeks of Kommutative Algebra) is not necessary, but helpful. Knowledge on algebraic topology (as in the course in WS 18/19) is not necessary, but helpful. Time/Date Mo 10--12; Thu 10--12 Location Mo M 102; Thu M 104 Course homepage https://www.uni-r.de/Fakultaeten/nat_Fak_I/loeh/teaching/grouphom_ss19 (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration Registration for course work/examination/ECTS: FlexNow Course work (Studienleistungen) Successful participation in the exercise classes: 50% of the credits, presentation of a solution in class Examination (Prüfungsleistungen) Oral exam: Duration: 25 minutes, Date: individual, re-exam: Date: individual Regelungen bei Studienbeginn vor WS 2015 / 16 Benotet: O. g. Studienleistung und o. g. Prüfungsleistung; die Note ergibt sich aus der Prüfungsleistung Unbenotet: O. g. Studienleistung Modules BV, MV, MArGeo, MGAGeo ECTS 9

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