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

Abstract

We make use of $\mathcal{F}$-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.

v2. added a reference and corrected a typo

References in corpus (1)

• Luttinger surgery and Kodaira dimension

Cited by in corpus (1)

• The Yamabe invariant of a class of symplectic manifolds