Title

New symplectic 4-manifolds with b+=1

Document Type

Article

Publication Date

11-1-2005

Abstract

In 1995 Dusa McDuff and Dietmar Salamon conjectured the existence of symplectic 4-manifolds (X, ω) which satisfy b = 1, K = 0, K · ω > 0, and which fail to be of Lefschetz type. This is equivalent to finding a symplectic, homology T × S manifold with nontorsion canonical class and a cohomology ring which is not isomorphic to the cohomology ring of T × S . They needed such examples to complete a list of possible symplectic 4-manifolds with b = 1. In that same year Tian-Jun Li and Ai-ko Liu, working from a different point of view, questioned whether there existed symplectic 4-manifolds with b = 1 with Seiberg-Witten invariants that did not depend on the chamber structure of the moduli space. The purpose of this paper is to construct an infinite number of examples which satisfy both requirements. - + + 2 2 2 2 2

Publication Source (Journal or Book title)

Mathematische Annalen

First Page

633

Last Page

643

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