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

Abstract

Abstract. 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.À 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.

The Yamabe invariant of a class of symplectic 4-manifolds

“…At the time when this paper was written, Suárez-Serrato and Torres [27] have posted a result on the computation of the Yamabe invariant for symplectic 4−manifolds of Kodaira dimension 0 and 1.…”