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On the Farrell–Jones Conjecture and its applications
Author(s) -
Bartels Arthur,
Lück Wolfgang,
Reich Holger
Publication year - 2008
Publication title -
journal of topology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.447
H-Index - 31
eISSN - 1753-8424
pISSN - 1753-8416
DOI - 10.1112/jtopol/jtm008
Subject(s) - mathematics , conjecture , mathematical economics , combinatorics
We present the status of the Farrell–Jones Conjecture for algebraic K ‐theory for a group G and arbitrary coefficient rings R . We add new groups for which the conjecture is known to be true, and we study inheritance properties. We discuss new applications, focussing on the Bass Conjecture, the Kaplansky Conjecture, and conjectures generalizing Moody's Induction Theorem. Thus, we considerably extend the class of groups for which these conjectures are known.