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Higher localised Â-genera: a note on disconnected fixed-point sets
Abstract
For a proper cocompact action of a finitely generated discrete group Γ on a spin manifold M, the higher localised Â-genera Âg(M,ω) introduced earlier by the author and Mathai were shown to be an obstruction to Γ-invariant metrics of positive scalar curvature, for ω arising from the subring of H*(underlineBΓ,ℝ) generated by elements of degree at most $2$, under the assumptions that the fixed-point set Mg is connected and that g is regular with respect to a certain real group $2$-cocycle. We show that both assumptions can be dropped.
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BibTeX
@misc{guo2026higher,
title = {{Higher localised $\widehatA$-genera: a note on disconnected fixed-point sets}},
author = {Hao Guo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07833},
eprint = {2610.07833},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07833},
}
RIS
TY - UNPB
TI - Higher localised Â-genera: a note on disconnected fixed-point sets
AU - Hao Guo
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.07833
UR - https://arxiv.org/abs/2610.07833
AB - For a proper cocompact action of a finitely generated discrete group Γ on a spin manifold M, the higher localised Â-genera Â_g(M,ω) introduced earlier by the author and Mathai were shown to be an obstruction to Γ-invariant metrics of positive scalar curvature, for ω arising from the subring of H^*(underlineBΓ,ℝ) generated by elements of degree at most $2$, under the assumptions that the fixed-point set M^g is connected and that g is regular with respect to a certain real group $2$-cocycle. We show that both assumptions can be dropped.
ER -