Algebraic K-theory over virtually abelian groups

作者:Quinn Frank*
来源:Journal of Pure and Applied Algebra, 2012, 216(1): 170-183.
DOI:10.1016/j.jpaa.2011.06.001

摘要

Controlled K-theory is used to show that algebraic K-theory of a group mapping to a virtually abelian group is described by an assembly map defined using hyperelementary subgroups (possibly infinite) of the target group. These subgroups are virtually cyclic, so the result is a refinement of the (fibered) Farrell-Jones conjecture that K-theory conies from virtually cyclic groups. A corollary is that for any group, the Farrell-Jones conjecture is equivalent to this refined version.

  • 出版日期2012-1
  • 单位Virginia Tech; 美国弗吉尼亚理工大学(Virginia Tech)