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Mazur manifolds and symplectic structures
Abstract
We use the Heegaard Floer homology cobordism maps to obstruct the existence of a symplectic structure on the Akbulut-Kirby Mazur manifolds whose boundary is a Brieskorn sphere Y among $Σ(2,3,13),$ Σ(2,5,7) and Σ(3,4,5). Furthermore, we describe how they imply the existence of exotic pairs of simply connected 4-manifolds, with definite intersection form, whose boundary is a Brieskorn sphere bounding a Mazur manifold.
Related
- Links of Mazur manifolds and exotica
- Fedosov manifolds with parallel symplectic Weyl curvature
- Symplectic four-manifolds and hyperbolic π-orbifolds
- The ECH and alternative ECH capacities of closed symplectic 4-manifolds
- Finite Symplectic Automorphisms of Hyperkähler Manifolds of K3[n]-Type Act Trivially on Discriminant Groups
BibTeX
@misc{cavallo2026mazur,
title = {{Mazur manifolds and symplectic structures}},
author = {Alberto Cavallo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.15095},
eprint = {2605.15095},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.15095},
}
RIS
TY - UNPB
TI - Mazur manifolds and symplectic structures
AU - Alberto Cavallo
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2605.15095
UR - https://arxiv.org/abs/2605.15095
AB - We use the Heegaard Floer homology cobordism maps to obstruct the existence of a symplectic structure on the Akbulut-Kirby Mazur manifolds whose boundary is a Brieskorn sphere Y among $Σ(2,3,13),$ Σ(2,5,7) and Σ(3,4,5). Furthermore, we describe how they imply the existence of exotic pairs of simply connected 4-manifolds, with definite intersection form, whose boundary is a Brieskorn sphere bounding a Mazur manifold.
ER -