Braided Multisections and Aspherical Stein Fillings
Abstract
We construct Stein fillings diffeomorphic to complements of a connected symplectic unbranched multisection and a regular sphere fiber in the ruled surface Σg× S2. For every g≥2 and every multisection degree p≥4, a fixed contact three-manifold admits infinitely many pairwise nonhomeomorphic aspherical fillings of this form. Their first and second integral homology groups are Z2g⊕Z/p and Z(2g−1)(p−1), respectively, and their intersection pairings vanish. We vary the braid monodromy while preserving the marked contact boundary. Unbounded torsion orders in the first homology of regular unbranched covers of degree p2p−1 detect infinitely many isomorphism types of fundamental groups. We also give an equivariant Weinstein handle construction for the cyclic filling Wg,4. The contact boundaries are supported by spinal open books with planar pages and have positive ordinary support genus.
Related
- Braided Multisections and Akhmedov's Fake Quadrics
- Braided Multisections and Symplectic Four-Manifolds with the Rational Cohomology of S2× S2
- Contact 3-manifolds with infinitely many rational homology ball Stein fillings
- Rigidity of multisections to the universal cubic plane curve
- Nonexistence of degree two rational multisections of conic bundles over the plane
BibTeX
@misc{akhmedov2026braided,
title = {{Braided Multisections and Aspherical Stein Fillings}},
author = {Anar Akhmedov},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01833},
eprint = {2611.01833},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01833},
note = {CC0},
}
RIS
TY - UNPB
TI - Braided Multisections and Aspherical Stein Fillings
AU - Anar Akhmedov
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01833
UR - https://arxiv.org/abs/2611.01833
AB - We construct Stein fillings diffeomorphic to complements of a connected symplectic unbranched multisection and a regular sphere fiber in the ruled surface Σ_g× S^2. For every g≥2 and every multisection degree p≥4, a fixed contact three-manifold admits infinitely many pairwise nonhomeomorphic aspherical fillings of this form. Their first and second integral homology groups are Z^2g⊕Z/p and Z^(2g−1)(p−1), respectively, and their intersection pairings vanish. We vary the braid monodromy while preserving the marked contact boundary. Unbounded torsion orders in the first homology of regular unbranched covers of degree p2^p−1 detect infinitely many isomorphism types of fundamental groups. We also give an equivariant Weinstein handle construction for the cyclic filling W_g,4. The contact boundaries are supported by spinal open books with planar pages and have positive ordinary support genus.
ER -