Homotopy type of the unitary group of the uniform Roe algebra on ${\mathbb{Z}}^n$

Tsuyoshi Kato, Daisuke Kishimoto, Mitsunobu Tsutaya

We study the homotopy type of the space of the unitary group $\U_1(C^\ast_u(|\mathbb{Z}^n|))$ of the uniform Roe algebra $C_u^{\ast }(|{\mathbb{Z}}^n|)$ of ${\mathbb{Z}}^n$. We show that…