PreprintCC BY 4.0arXiv
The real quotient of the Cartwright-Steger surface
Abstract
Borisov and Yeung showed that the Cartwright-Steger surface X is defined over ℚ, hence complex conjugation gives an antiholomorphic involution on X. We show that the orbit space Y is a closed oriented smooth four-manifold homeomorphic to ℂℙ2# (S1 × S3), presenting X as a double branched cover X→ Y, with branch locus diffeomorphic to the connected sum of three copies of the real projective plane.
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BibTeX
@misc{stipsicz2026real,
title = {{The real quotient of the Cartwright-Steger surface}},
author = {András I. Stipsicz and Zoltán Szabó},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.09207},
eprint = {2609.09207},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09207},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The real quotient of the Cartwright-Steger surface
AU - András I. Stipsicz
AU - Zoltán Szabó
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2609.09207
UR - https://arxiv.org/abs/2609.09207
AB - Borisov and Yeung showed that the Cartwright-Steger surface X is defined over ℚ, hence complex conjugation gives an antiholomorphic involution on X. We show that the orbit space Y is a closed oriented smooth four-manifold homeomorphic to ℂℙ^2# (S^1 × S^3), presenting X as a double branched cover X→ Y, with branch locus diffeomorphic to the connected sum of three copies of the real projective plane.
ER -