Mathematics – K-Theory and Homology
Scientific paper
2011-11-30
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.
Ramras Daniel A.
Tessera Romain
Yu Guoliang
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