A note on collapse, entropy, and vanishing of the Yamabe invariant of symplectic 4-manifolds

作者：Suarez Serrato Pablo; Torres Rafael^*

来源：Journal of Geometry and Physics, 2014, 86: 383-391.

DOI：10.1016/j.geomphys.2014.09.001

• F-structures
• Yamabe invariant
• Minimal entropy
• Symplectic 4-manifolds

We make use of F-structures and technology developed by Paternain-Petean to compute minimal entropy, minimal volume, and Yamabe invariant of symplectic 4-manifolds, as well as to study their collapse with sectional curvature bounded from below. A la Gompf, we show that these invariants vanish on symplectic 4-manifolds that realize any given finitely presented group as their fundamental group. We extend to the symplectic realm a result of LeBrun which relates the Kodaira dimension with the Yamabe invariant of compact complex surfaces.

• 出版日期2014-12