Finite decomposition complexity and the integral Novikov conjecture for higher algebraic K-theory Academic Article uri icon

abstract

  • 2014 by De Gruyter. 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.

published proceedings

  • Journal fr die reine und angewandte Mathematik (Crelles Journal)

author list (cited authors)

  • Ramras, D. A., Tessera, R., & Yu, G.

citation count

  • 19

complete list of authors

  • Ramras, Daniel A||Tessera, Romain||Yu, Guoliang

publication date

  • January 2014