English

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 KK-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

R2 v1 2026-06-22T18:12:10.554Z