TY - JOUR
T1 - Homotopy type of the unitary group of the uniform Roe algebra on Zn
AU - Kato, Tsuyoshi
AU - Kishimoto, Daisuke
AU - Tsutaya, Mitsunobu
N1 - Publisher Copyright:
© 2023 World Scientific Publishing Co. Pte Ltd. All rights reserved.
PY - 2023/6/1
Y1 - 2023/6/1
N2 - 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.
AB - 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.
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U2 - 10.1142/S1793525321500357
DO - 10.1142/S1793525321500357
M3 - Article
AN - SCOPUS:85104929626
SN - 1793-5253
VL - 15
SP - 495
EP - 512
JO - Journal of Topology and Analysis
JF - Journal of Topology and Analysis
IS - 2
ER -