Finite decomposition complexity and the integral Novikov conjecture for higher algebraic K-theory

Details Finite decomposition complexity and the integral Novikov conjecture for higher algebraic K-theory Finite decomposition complexity and the integral Novikov conjecture for higher algebraic K-theory

2011-11-30

arxiv.org/abs/1111.7022v2

Mathematics

K-Theory and Homology

51 pages. Version 2 corrects an error in Lemma 6.17. This requires an adjustment to Definition 4.10 and two new lemmas (5.4 an

Scientific paper

Decomposition complexity for metric spaces was recently introduced by Guentner, Tessera, and Yu as a natural generalization of asymptotic dimension. We prove a vanishing result for the continuously controlled algebraic K-theory of bounded geometry metric spaces with finite decomposition complexity. This leads to a proof of the integral K-theoretic Novikov conjecture, regarding split injectivity of the K-theoretic assembly map, for groups with finite decomposition complexity and finite CW models for their classifying spaces. By work of Guentner, Tessera, and Yu, this includes all (geometrically finite) linear groups.

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