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Deformation of singular fibers of genus two fibrations and small exotic symplectic 4-manifolds

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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:… Click to show full abstract

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.

Keywords: fibers genus; singular fibers; formula see; see text; genus two

Journal Title: International Journal of Mathematics
Year Published: 2019

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