PreprintCC BY 4.0arXiv
Symplectic four-manifolds and hyperbolic π-orbifolds
Abstract
We construct closed symplectic 4-manifolds admitting the structure of hyperbolic π-orbifold, addressing LeBrun's conjecture. Our simplest example has Euler characteristic $304$, is tessellated by $64$ copies of the right-angled hyperbolic $120$-cell and admits a four-fold branched covering over a product of two surfaces of genus $4$.
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BibTeX
@misc{lin2026symplectic,
title = {{Symplectic four-manifolds and hyperbolic $π$-orbifolds}},
author = {Francesco Lin and Bruno Martelli},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15698},
eprint = {2610.15698},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15698},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Symplectic four-manifolds and hyperbolic π-orbifolds
AU - Francesco Lin
AU - Bruno Martelli
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15698
UR - https://arxiv.org/abs/2610.15698
AB - We construct closed symplectic 4-manifolds admitting the structure of hyperbolic π-orbifold, addressing LeBrun's conjecture. Our simplest example has Euler characteristic $304$, is tessellated by $64$ copies of the right-angled hyperbolic $120$-cell and admits a four-fold branched covering over a product of two surfaces of genus $4$.
ER -