Algebraic $K$-theory, assembly maps, controlled algebra, and trace methods
K-Theory and Homology
2018-04-19 v3 Algebraic Topology
Geometric Topology
Abstract
We give a concise introduction to the Farrell-Jones Conjecture in algebraic -theory and to some of its applications. We survey the current status of the conjecture, and we illustrate the two main tools that are used to attack it: controlled algebra and trace methods.
Cite
@article{arxiv.1702.02218,
title = {Algebraic $K$-theory, assembly maps, controlled algebra, and trace methods},
author = {Holger Reich and Marco Varisco},
journal= {arXiv preprint arXiv:1702.02218},
year = {2018}
}
Comments
Final version, to appear in Space - Time - Matter. Analytic and Geometric Structures (Jochen Br\"uning and Matthias Staudacher, eds.), De Gruyter. v3: updated references, added index, fixed few typos. 44 pages