Uniqueness of Symplectic Canonical Class, Surface Cone and Symplectic Cone of 4-Manifolds with B+ = 1

By Tian-Jun Li, A. Liu. 2000

124 citations recorded by the source corpus.

Let M be a closed oriented smooth 4-manifold admitting symplectic structures. If M is minimal and has b^+=1, we prove that there is a unique symplectic canonical class up to sign, and any real second cohomology class of positive square is represented by symplectic forms. Similar results hold when M is not minimal.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/76b7811addb2f53cd1f029a656943a3eb0c150f8

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In Geometry and Topology

1. D. Mcduff
2. Weiyi Zhang
3. Tian-Jun Li
4. F. Schlenk
5. Michael Hutchings
6. Yong-Geun Oh
7. Y. Ostrover
8. S. Bauer

Citations in the corpus

• Symplectic embeddings of 4‐dimensional ellipsoids (2008, background): “To do this, first place ε0 so that it meets the x axis at x0 := (n−δ0, 0) for small δ0 > 0 and make the first cut 1 so that it meets the y axis at y1 := (0,m− δ0− δ1) for small δ1 > 0.”
• Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds (2007, background): “A complete description for the symplectic cone of all the 4-manifolds with b+ = 1 was subsequently given in [21].”