Splitting formulas for certain Waldhausen Nil-groups
K-Theory and Homology
2014-02-26 v1 Algebraic Topology
Abstract
For a group G that splits as an amalgamation of A and B over a common subgroup C, there is an associated Waldhausen Nil-group, measuring the "failure" of Mayer-Vietoris for algebraic K-theory. Assume that (1) the amalgamation is acylindrical, and (2) the groups A,B,G satisfy the Farrell-Jones isomorphism conjecture. Then we show that the Waldhausen Nil-group splits as a direct sum of Nil-groups 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.
Cite
@article{arxiv.0711.2533,
title = {Splitting formulas for certain Waldhausen Nil-groups},
author = {J. -F. Lafont and I. J. Ortiz},
journal= {arXiv preprint arXiv:0711.2533},
year = {2014}
}
Comments
12 pages