PreprintCC0arXiv
Symplectic Surface Summing and Negative Spheres
Abstract
We extend the sphere-summing construction of \cite{AZ} from torus sums of spheres to symplectic sums along surfaces of arbitrary genus. The relative surfaces may have arbitrary positive intersection number with the summing surface. We give formulas for the genus and self-intersection of the resulting surface, together with graph and simultaneous versions of the construction. The original elliptic-surface case is recovered as a special case, and higher-genus examples are obtained from hyperelliptic Lefschetz fibrations and braided symplectic surfaces in Σh× S2.
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BibTeX
@misc{akhmedov2026symplectic,
title = {{Symplectic Surface Summing and Negative Spheres}},
author = {Anar Akhmedov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11803},
eprint = {2609.11803},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11803},
note = {CC0},
}
RIS
TY - UNPB
TI - Symplectic Surface Summing and Negative Spheres
AU - Anar Akhmedov
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11803
UR - https://arxiv.org/abs/2609.11803
AB - We extend the sphere-summing construction of \cite{AZ} from torus sums of spheres to symplectic sums along surfaces of arbitrary genus. The relative surfaces may have arbitrary positive intersection number with the summing surface. We give formulas for the genus and self-intersection of the resulting surface, together with graph and simultaneous versions of the construction. The original elliptic-surface case is recovered as a special case, and higher-genus examples are obtained from hyperelliptic Lefschetz fibrations and braided symplectic surfaces in Σ_h× S^2.
ER -