TY - JOUR
T1 - HOMOTOPY TYPE OF THE SPACE OF FINITE PROPAGATION UNITARY OPERATORS ON Z
AU - Kato, Tsuyoshi
AU - Kishimoto, Daisuke
AU - Tsutaya, Mitsunobu
N1 - Publisher Copyright:
© 2023, International Press. Permission to copy for private use granted.
PY - 2023
Y1 - 2023
N2 - The index theory for the space of finite propagation unitary operators was developed by Gross, Nesme, Vogts and Werner from the viewpoint of quantum walks in mathematical physics. In particular, they proved that π0 of the space is determined by the index. However, nothing is known about the higher homotopy groups. In this article, we describe the homotopy type of the space of finite propagation unitary operators on the Hilbert space of square summable C-valued Z-sequences, so we can determine its homotopy groups. We also study the space of (end-)periodic finite propagation unitary operators.
AB - The index theory for the space of finite propagation unitary operators was developed by Gross, Nesme, Vogts and Werner from the viewpoint of quantum walks in mathematical physics. In particular, they proved that π0 of the space is determined by the index. However, nothing is known about the higher homotopy groups. In this article, we describe the homotopy type of the space of finite propagation unitary operators on the Hilbert space of square summable C-valued Z-sequences, so we can determine its homotopy groups. We also study the space of (end-)periodic finite propagation unitary operators.
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U2 - 10.4310/HHA.2023.V25.N1.A20
DO - 10.4310/HHA.2023.V25.N1.A20
M3 - Article
AN - SCOPUS:85160726088
SN - 1532-0073
VL - 25
SP - 375
EP - 400
JO - Homology, Homotopy and Applications
JF - Homology, Homotopy and Applications
IS - 1
ER -