PreprintarXiv licencearXiv
On Auroux's Luttinger-surgery uniqueness question
Abstract
We construct simply connected integral symplectic four-manifolds forming an exotic pair, with equal values of c12, c2, c1mathbin·[ω], and [ω]2, but with symplectic Kodaira dimensions −∞ and $2$. Since symplectic Kodaira dimension is invariant under Luttinger surgery, the two manifolds are not Luttinger-surgery equivalent. This gives a negative answer to Auroux's uniqueness question.
Related
BibTeX
@misc{iida2026aurouxs,
title = {{On Auroux's Luttinger-surgery uniqueness question}},
author = {Nobuo Iida},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29561},
eprint = {2609.29561},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29561},
}
RIS
TY - UNPB
TI - On Auroux's Luttinger-surgery uniqueness question
AU - Nobuo Iida
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.29561
UR - https://arxiv.org/abs/2609.29561
AB - We construct simply connected integral symplectic four-manifolds forming an exotic pair, with equal values of c_1^2, c_2, c_1mathbin·[ω], and [ω]^2, but with symplectic Kodaira dimensions −∞ and $2$. Since symplectic Kodaira dimension is invariant under Luttinger surgery, the two manifolds are not Luttinger-surgery equivalent. This gives a negative answer to Auroux's uniqueness question.
ER -