PreprintCC BY 4.0arXiv
Classical cylindrical contact homology is not invariant over bZ
Abstract
We show that classical cylindrical contact homology over ℤ, equipped with its decomposition by free homotopy classes, is not invariant under changes of hypertight contact form. Specifically, we construct two nondegenerate hypertight perturbations of the standard Seifert contact form on Σ(2,4,5) whose cylindrical contact homologies in the regular-fiber class are respectively torsion-free and contain ℤ/5-torsion.
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BibTeX
@misc{chanda2026classical,
title = {{Classical cylindrical contact homology is not invariant over $\bZ$}},
author = {Soham Chanda},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11189},
eprint = {2610.11189},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11189},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Classical cylindrical contact homology is not invariant over bZ
AU - Soham Chanda
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11189
UR - https://arxiv.org/abs/2610.11189
AB - We show that classical cylindrical contact homology over ℤ, equipped with its decomposition by free homotopy classes, is not invariant under changes of hypertight contact form. Specifically, we construct two nondegenerate hypertight perturbations of the standard Seifert contact form on Σ(2,4,5) whose cylindrical contact homologies in the regular-fiber class are respectively torsion-free and contain ℤ/5-torsion.
ER -