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Assembly maps and coarse geometry SemesterSoSe 2019 Dozent/in Ulrich Bunke Veranstaltungsart Vorlesung Inhalt The goal of this lecture course is to explain a proof of the Farrell-Jones conjecture for hyperbolic groups. Our argument is inspired by the original proof by Barthels-Reich-Lück, but we will rephrase it in terms of the language of coarse homotopy theory. In greater details the course will discuss the following: - the orbit category of a group, families of subgroups and some equivariant homotopy theory - construction of interesting functors from the orbit category - assembly maps - the category of bornological coarse spaces - coarse homology theories (definition, examples, motives) - hybrid structures (how to embed topology into coarse geometry), homotopy and excision - a detailed proof of the Farrell-Jones conjecture (stating that the assembly for equivariant algebraic K-theory and the family of virtually cyclic subgroups is an equivalence) if the group is hyperbolic Literaturangaben We will give pointers to the literature during the course. But in order to get an idea what the course is about one could have a look at the papers by Barthels-Reich-Lück in order to see the statement and applications of the Farrell-Jones conjecture. In order to see the language I want to explain in the lectures (which will differ considerably from BRL) and level of the course I refer to the papers on coarse homotopy with A. Engel, D. Kasprowski and Ch. Winges from the last years. Empfohlene Vorkenntnisse The course requires some experience with the language infinity categories. Coarse geometry and homotopy theory will be introduced from scratch. Termin Do 10-12 Ort M102 Anmeldung
MV, MArGeo, MGAGeo ECTS 3 |