Finite decomposition complexity and the integral Novikov conjecture for higher algebraic K-theory
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Daniel A. Ramras
,
Romain Tessera
Abstract
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.
Funding source: NSF grants
Award Identifier / Grant number: DMS-0804553, DMS-0968766, DMS-0706486, DMS-0600216, DMS-1101195
Funding source: ANR grants
Award Identifier / Grant number: AGORA, BLANC
We thank Daniel Kasprowski for pointing out an error in a previous version of the paper, and the referee for offering many suggestions that improved the exposition. The first author also thanks Ben Wieland for helpful conversations.
© 2014 by De Gruyter
Articles in the same Issue
- Frontmatter
- The Oseen–Navier–Stokes flow in the exterior of a rotating obstacle: The non-autonomous case
- Macdonald formula for curves with planar singularities
- Geometry of orbit spaces of proper Lie groupoids
- Lefschetz trace formula for open adic spaces
- Finite decomposition complexity and the integral Novikov conjecture for higher algebraic K-theory
- Almost harmonic Maass forms and Kac–Wakimoto characters
- Optimal isoperimetric inequalities for complete proper minimal submanifolds in hyperbolic space
- Unique Cartan decomposition for II1 factors arising from arbitrary actions of hyperbolic groups
- Addendum: Hybrid bounds for twisted L-functions
Articles in the same Issue
- Frontmatter
- The Oseen–Navier–Stokes flow in the exterior of a rotating obstacle: The non-autonomous case
- Macdonald formula for curves with planar singularities
- Geometry of orbit spaces of proper Lie groupoids
- Lefschetz trace formula for open adic spaces
- Finite decomposition complexity and the integral Novikov conjecture for higher algebraic K-theory
- Almost harmonic Maass forms and Kac–Wakimoto characters
- Optimal isoperimetric inequalities for complete proper minimal submanifolds in hyperbolic space
- Unique Cartan decomposition for II1 factors arising from arbitrary actions of hyperbolic groups
- Addendum: Hybrid bounds for twisted L-functions
