PreprintCC BY 4.0arXiv
Systolic pants decompositions with polynomial growth
Abstract
We investigate improved bounds on the kissing number of a hyperbolic surface under the assumption that the systole set contains pants decompositions with volume growth constraints. Namely, when the dual graph of the pants decomposition has polynomial volume growth, we obtain a power-savings improvement for the upper bound on the kissing number in terms of systolic length. We also construct super-exponentially many (in g) pants decompositions with exponential volume growth for which our techniques still imply stronger upper bounds for kissing numbers. The proofs use the technology of ``stem systems'' and ``tulips'' developed by the first and second author to study $1$-systems of curves.
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BibTeX
@misc{aougab2026systolic,
title = {{Systolic pants decompositions with polynomial growth}},
author = {Tarik Aougab and Jonah Gaster and Nicholas Miller},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37551},
eprint = {2610.37551},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37551},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Systolic pants decompositions with polynomial growth
AU - Tarik Aougab
AU - Jonah Gaster
AU - Nicholas Miller
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37551
UR - https://arxiv.org/abs/2610.37551
AB - We investigate improved bounds on the kissing number of a hyperbolic surface under the assumption that the systole set contains pants decompositions with volume growth constraints. Namely, when the dual graph of the pants decomposition has polynomial volume growth, we obtain a power-savings improvement for the upper bound on the kissing number in terms of systolic length. We also construct super-exponentially many (in g) pants decompositions with exponential volume growth for which our techniques still imply stronger upper bounds for kissing numbers. The proofs use the technology of ``stem systems'' and ``tulips'' developed by the first and second author to study $1$-systems of curves.
ER -