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Fakultät für Mathematik Universität Regensburg
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Assembly maps and coarse geometry
Semester
SoSe 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
  • Anmeldung zu Studienleistungen/Prüfungsleistungen: FlexNow
Studienleistungen
  • Fachgespräch: Dauer: 30 min, Termin: Nach Vereinbarung
Prüfungsleistungen
  • Mündliche Prüfung: Dauer: 30 min, Termin: nach Vereinbarung,
    Wiederholungsprüfung: Termin:
Module
MV, MArGeo, MGAGeo

ECTS
3
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