Simply connected minimal symplectic 4-manifolds with signature less than - 1

Anar Akhmedov; Scott Baldridge; R. Inanç Baykur; Paul Kirk; B. Doug Park

doi:10.4171/jems/192

Simply connected minimal symplectic 4-manifolds with signature less than - 1

Anar Akhmedov, Scott Baldridge, R. Inanç Baykur, Paul Kirk, B. Doug Park

Mathematics

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

18 Scopus citations

Abstract

For each pair (e,σ) of integers satisfying 2e + 3σ ≥ 0, σ ≤ - 2, and e + σ ≡0 (mod 4), with four exceptions, we construct a minimal, simply connected symplectic 4-manifold with Euler characteristic e and signature σ. We also produce simply connected, minimal symplectic 4-manifolds with signature zero (resp. signature-1) with Euler characteristic 4k (resp. 4k + 1) for all k ≥ 46 (resp. k ≥ 49).

Original language	English (US)
Pages (from-to)	133-161
Number of pages	29
Journal	Journal of the European Mathematical Society
Volume	12
Issue number	1
DOIs	https://doi.org/10.4171/jems/192
State	Published - 2010

Keywords

4-manifold
Fundamental group
Luttinger surgery
Symplectic topology

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AU - Park, B. Doug

PY - 2010

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AB - For each pair (e,σ) of integers satisfying 2e + 3σ ≥ 0, σ ≤ - 2, and e + σ ≡0 (mod 4), with four exceptions, we construct a minimal, simply connected symplectic 4-manifold with Euler characteristic e and signature σ. We also produce simply connected, minimal symplectic 4-manifolds with signature zero (resp. signature-1) with Euler characteristic 4k (resp. 4k + 1) for all k ≥ 46 (resp. k ≥ 49).

KW - 4-manifold

KW - Fundamental group

KW - Luttinger surgery

KW - Symplectic topology

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Simply connected minimal symplectic 4-manifolds with signature less than - 1

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