Splitting With Continuous Control in Algebraic K-theory

David Rosenthal

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Splitting With Continuous Control in Algebraic K-theory

David Rosenthal

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Abstract

In this work, the continuously controlled assembly map in algebraic $K$-theory, as developed by Carlsson and Pedersen, is proved to be a split injection for groups $Γ$ that satisfy certain geometric conditions. The group $Γ$ is allowed to have torsion, generalizing a result of Carlsson and Pedersen. Combining this with a result of John Moody, $K_0(kΓ)$ is proved to be isomorphic to the colimit of $K_0(kH)$ over the finite subgroups $H$ of $Γ$, when $Γ$ is a virtually polycyclic group and $k$ is a field of characteristic zero.

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BibTeX RIS

David Rosenthal. 2003-09-05. Splitting With Continuous Control in Algebraic K-theory. https://arxiv.org/abs/math/0309106

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