Year: 2026
Type: preprint
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 $Σ_h\times S^2$.
Source: arXiv (Cornell University)
Author: Akhmedov, Anar
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212316310