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Die folgenden Informationen sind noch nicht freigegeben und deshalb unverbindlich: Coarse Geometry SemesterWiSe 2025 / 26 Lecturer Ulrich Bunke Type of course (Veranstaltungsart) Seminar German title Grobe Geometrie Contents While topologies describe local properties of spaces near points, coarse structures are used to encode large scale properties. Metric spaces have both flavours together. Similarly as taking the underlying topological space of a metric space coarse geometry considers the underlying coarse space represented by the metric space. While the natural morphisms in metric geometry are isometries, in topology we consider the much more general notion of continuous maps, and likewise in coarse geometry we go over to the much more flexible notion of coarse mapa. Coarse geometry has important applications to geometric group theory, index theory, and also in mathematical physics. In this seminar we will start from scratch and introduce the basic notions of coarse geometry. We will construct and study the category of bornological coarse space and present interesting objects therein. We will go first steps towards coarse homotopy theory by describing various coarsely invariant concepts and coarse invariants leading to the notion of a coarse homology theory. We will connect with applications to geometric group theory and global analysis by discussing the canonical coarse structure on groups and ($C^{*}$-)algebras naturally associated to coarse spaces. The first few talks just build on set theory language and are very suitable for Bachelor/Lehramts students https://bunke.app.uni-regensburg.de/seminarCoarse-1.pdf Literature the classical books by J. Roe, the basic notions are explained in the book by Bunke-Engel whose elementary sections are the basis of this seminar, a research level overview can be found in https://arxiv.org/abs/2305.09203 Recommended previous knowledge metric spaces, topological spaces Time/Date M 103, 14-16 Mo Course homepage https://elearning.uni-regensburg.de/course/view.php?id=71751 (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration
BSem, MV, MSem, LA-GySem ECTS 4,5 |