On a quantitative operator K-theory

By H. Oyono-Oyono, Guoliang Yu. 2011

68 citations recorded by the source corpus.

In this paper, we develop a quantitative K-theory for filtered C*-algebras. Particularly interesting examples of filtered C*-algebras include group C*-algebras, crossed product C*-algebras and Roe algebras. We prove a quantitative version of the six term exact sequence and a quantitative Bott periodicity. We apply the quantitative K-theory to formulate a quantitative version of the Baum-Connes conjecture and prove that the quantitative Baum-Connes conjecture holds for a large class of groups.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1da32e6ad2e4d1531a315d012838800ec70db0e1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Romain Tessera
2. Daniel A. Ramras
3. Guoliang Yu
4. Rufus Willett
5. Zhizhang Xie

In Mathematical Physics

1. Daniel A. Ramras
2. Romain Tessera
3. Guoliang Yu
4. Assaf Naor
5. Rufus Willett
6. Martin Finn-Sell
7. Yuval Peres
8. E. Guentner

Citations in the corpus

• Finite decomposition complexity and the integral Novikov conjecture for higher algebraic K-theory (2011, methodology): “be possible to construct quantitative versions of higher algebraic K–groups (analogous to the Ranicki–Yamasaki controlled lower K–groups, and to recent work of Oyono-Oyono and Yu in operator K–theory [20]) such a theory does not currently exist. Instead, we produce analogous (strictly exact) Mayer– ”