PreprintCC BY-NC-ND 4.0HAL
Roe algebras and coarse index maps for spaces with proper actions of étale groupoids. II
Abstract
Building on the Roe algebra framework developed in the first paper of this series, we construct equivariant coarse index maps for locally compact Hausdorff spaces equipped with proper actions of étale groupoids, with coefficients in any separable groupoid C* -algebra. The construction uses the coarse structures determined by the groupoid action and requires no choice of metric. By identifying Roe algebras of canonical modules with reduced crossed products, we prove that the Baum-Connes assembly map with coefficients factors through the coarse index map.
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BibTeX
@misc{mao2026algebras,
title = {{Roe algebras and coarse index maps for spaces with proper actions of étale groupoids. II}},
author = {Kai Mao},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29879},
eprint = {2610.29879},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05826186v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Roe algebras and coarse index maps for spaces with proper actions of étale groupoids. II
AU - Kai Mao
PY - 2026
DA - 2026/10/20
PB - HAL
DO - 10.48550/arxiv.2610.29879
UR - https://hal.science/hal-05826186v1
AB - Building on the Roe algebra framework developed in the first paper of this series, we construct equivariant coarse index maps for locally compact Hausdorff spaces equipped with proper actions of étale groupoids, with coefficients in any separable groupoid C* -algebra. The construction uses the coarse structures determined by the groupoid action and requires no choice of metric. By identifying Roe algebras of canonical modules with reduced crossed products, we prove that the Baum-Connes assembly map with coefficients factors through the coarse index map.
ER -