We study the homotopy type of the space of the unitary group U1(C* u(|Zn|)) of the uniform Roe algebra C* u(|Zn|) of Zn. We show that the stabilizing map U1(C* u(|Zn|)) ? U8(C* u(|Zn|)) is a homotopy equivalence. Moreover, when n = 1, 2, we determine the homotopy type of U1(C* u(|Zn|)), which is the product of the unitary group U1(C*(|Zn|)) (having the homotopy type of U8(C) or Z B U8(C) depending on the parity of n) of the Roe algebra C*(|Zn|) and rational Eilenberg-MacLane spaces;copy 2023 World Scientific Publishing Company.
All Science Journal Classification (ASJC) codes
- Geometry and Topology