2019/01/30 by Anar Akhmedov, Sümeyra Sakallı, Sümeyra Sakalli
Mathematics · #Construct (python library) #Deformation (meteorology) #Diffeomorphism #Genus #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Simple (philosophy) #Symplectic geometry #Symplectomorphism #math.AG #math.GT #math.SG
paper · pdf · doi:10.1142/s0129167x19500174
published as International Journal of Mathematics, Volume 30, Issue number, 2019 · 38 pages, 14 figures. arXiv admin note: text overlap with arXiv:math/0507006 by other authors
arxiv created 2019/01/30 · openalex created_date 2019/02/21 · openalex publication_date 2019/02/28 · arxiv updated 2021/02/17 · openalex updated_date 2026/08/05
We introduce the [Formula: see text]-nodal spherical deformation of certain singular fibers of genus two fibrations, and use such deformations to construct various examples of simply connected minimal symplectic [Formula: see text]-manifolds with small topology. More specifically, we construct new exotic minimal symplectic [Formula: see text]-manifolds homeomorphic but not diffeomorphic to [Formula: see text], [Formula: see text], and [Formula: see text] for [Formula: see text] using combinations of such deformations, symplectic blowups, and (generalized) rational blowdown surgery. We also discuss generalizing our constructions to higher genus fibrations using [Formula: see text]-nodal spherical deformations of certain singular fibers of genus [Formula: see text] fibrations.