We study the homotopy type of the space of the unitary group U1(Cu) of the uniform Roe algebra Cu(|;n|) of &n. We show that the stabilizing map U1(Cu(|;n|)) U (Cu()) is a homotopy equivalence. Moreover, when n = 1, 2, we determine the homotopy type of U1(Cu(|;n|)), which is the product of the unitary group U1(C()) (having the homotopy type of U or ; × BU depending on the parity of n) of the Roe algebra C() and rational Eilenberg-MacLane spaces. ;copy 2021 World Scientific Publishing Company.
All Science Journal Classification (ASJC) codes
- Geometry and Topology