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Hinweis Bitte informieren Sie sich auf den jeweiligen GRIPS-Seiten über den digitalen Ablauf der Lehrveranstaltungen.  Note For our digital courses all relevant information can be found on the appropriate GRIPS sites.Introduction to instanton gauge theory SemesterSoSe 2021 Lecturer Raphael Zentner Type of course (Veranstaltungsart) Vorlesung Contents We will give an introduction to instanton gauge theory: Moduli spaces of ASD connections on closed 4-manifolds, and also Floer homology of 3-manifolds. Our aim is to introduce the basic analytical tools, in particular, the correct analytical setup, the linearisation of the equations, Fredholm theory, and the basic compactness properties - the Uhlenbeck compactification of the moduli spaces on closed 4-manifolds, and the somewhat more difficult case for manifolds with cylindrical ends, where "energy can escape down the end". The plan is to then introduce Floer homology, and, hopefully, to prove the surgery exact triangle. Literature S. Donaldson, Floer homology groups in Yang-Mills theory S. Donaldson, P. Kronheimer, Geometry of four-manifolds Recommended previous knowledge Analysis I-IV, and basic algebraic topology is certainly helpful. Time/Date Do 10-12 Uhr, Übungen/Exercise class Di 14-16 Uhr Location online Registration
MV ECTS 6 Leistungspunkte |