Continuous Control and the Algebraic L-theory Assembly Map

Details Continuous Control and the Algebraic L-theory Assembly Map Continuous Control and the Algebraic L-theory Assembly Map

2003-12-02

arxiv.org/abs/math/0312046v1

Forum Math. 18 (2006), no. 2, 193--209

Mathematics

Algebraic Topology

15 pages

Scientific paper

In this work, the assembly map in L-theory for the family of finite subgroups is proven to be a split injection for a class of groups. Groups in this class, including virtually polycyclic groups, have universal spaces that satisfy certain geometric conditions. The proof follows the method developed by Carlsson-Pedersen to split the assembly map in the case of torsion free groups. Here, the continuously controlled techniques and results are extended to handle groups with torsion.

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