PreprintCC BY 4.0arXiv
A Counterexample to Three Conjectures of Luo
Abstract
We give a single counterexample to Conjectures 1--3 as stated in Luo's paper: a minimal two-tetrahedron triangulation of the lens space L(3,1) with a null-homotopic loop edge. The proof uses quadrilateral matching equations, an explicit calculation of shape parameters, and known results on volume maximization.
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BibTeX
@misc{guo2026counterexample,
title = {{A Counterexample to Three Conjectures of Luo}},
author = {Qilong Guo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13979},
eprint = {2610.13979},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13979},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Counterexample to Three Conjectures of Luo
AU - Qilong Guo
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.13979
UR - https://arxiv.org/abs/2610.13979
AB - We give a single counterexample to Conjectures 1--3 as stated in Luo's paper: a minimal two-tetrahedron triangulation of the lens space L(3,1) with a null-homotopic loop edge. The proof uses quadrilateral matching equations, an explicit calculation of shape parameters, and known results on volume maximization.
ER -