Splitting formulas for certain Waldhausen Nilgroups
Abstract
For a group G that splits as an amalgamation of A and B over a common subgroup C, there is an associated Waldhausen Nilgroup, measuring the "failure" of MayerVietoris for algebraic Ktheory. Assume that (1) the amalgamation is acylindrical, and (2) the groups A,B,G satisfy the FarrellJones isomorphism conjecture. Then we show that the Waldhausen Nilgroup splits as a direct sum of Nilgroups associated to certain (explicitly describable) infinite virtually cyclic subgroups of G. We note that a special case of an acylindrical amalgamation includes any amalgamation over a finite group C.
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.2533
 Bibcode:
 2007arXiv0711.2533L
 Keywords:

 Mathematics  KTheory and Homology;
 Mathematics  Algebraic Topology
 EPrint:
 12 pages