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

JOURNAL OF GEOMETRY AND PHYSICS

卷:86

Article

Suarez-Serrato, Pablo¹  Torres, Rafael² 

[1] Univ Nacl Autonoma Mexico, Inst Matemat, Mexico City 04510, DF, Mexico

[2] Scuola Int Super Studi Avanzati, I-34136 Trieste, Italy

关键词: F-structures;    Yamabe invariant;    Minimal entropy;    Symplectic 4-manifolds;   

DOI  :  10.1016/j.geomphys.2014.09.001

来源: Elsevier

【 摘 要 】

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. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free