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

Anar Akhmedov; Sümeyra Sakalll

doi:10.1142/S0129167X19500174

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

Anar Akhmedov, Sümeyra Sakalll

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We introduce the 2-nodal spherical deformation of certain singular fibers of genus two fibrations, and use such deformations to construct various examples of simply connected minimal symplectic 4-manifolds with small topology. More specifically, we construct new exotic minimal symplectic 4-manifolds homeomorphic but not diffeomorphic to ℂℙ ² #6ℂℙ ² , ℂℙ ² #7ℂℙ ² , and 3ℂℙ ² #kℂℙ ² for k = 16, 17, 18, 19 using combinations of such deformations, symplectic blowups, and (generalized) rational blowdown surgery. We also discuss generalizing our constructions to higher genus fibrations using g-nodal spherical deformations of certain singular fibers of genus g ≥ 3 fibrations.

Original language	English (US)
Article number	1950017
Journal	International Journal of Mathematics
Volume	30
Issue number	3
DOIs	https://doi.org/10.1142/S0129167X19500174
State	Published - Mar 1 2019

Keywords

Lefschetz fibration
Symplectic 4-manifold
genus two fibration
mapping class group
rational blowdown

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10.1142/S0129167X19500174

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title = "Deformation of singular fibers of genus two fibrations and small exotic symplectic 4 -manifolds",

abstract = " We introduce the 2-nodal spherical deformation of certain singular fibers of genus two fibrations, and use such deformations to construct various examples of simply connected minimal symplectic 4-manifolds with small topology. More specifically, we construct new exotic minimal symplectic 4-manifolds homeomorphic but not diffeomorphic to ℂℙ 2 #6ℂℙ 2 , ℂℙ 2 #7ℂℙ 2 , and 3ℂℙ 2 #kℂℙ 2 for k = 16, 17, 18, 19 using combinations of such deformations, symplectic blowups, and (generalized) rational blowdown surgery. We also discuss generalizing our constructions to higher genus fibrations using g-nodal spherical deformations of certain singular fibers of genus g ≥ 3 fibrations. ",

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AU - Sakalll, Sümeyra

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N2 - We introduce the 2-nodal spherical deformation of certain singular fibers of genus two fibrations, and use such deformations to construct various examples of simply connected minimal symplectic 4-manifolds with small topology. More specifically, we construct new exotic minimal symplectic 4-manifolds homeomorphic but not diffeomorphic to ℂℙ 2 #6ℂℙ 2 , ℂℙ 2 #7ℂℙ 2 , and 3ℂℙ 2 #kℂℙ 2 for k = 16, 17, 18, 19 using combinations of such deformations, symplectic blowups, and (generalized) rational blowdown surgery. We also discuss generalizing our constructions to higher genus fibrations using g-nodal spherical deformations of certain singular fibers of genus g ≥ 3 fibrations.

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KW - Lefschetz fibration

KW - Symplectic 4-manifold

KW - genus two fibration

KW - mapping class group

KW - rational blowdown

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