3-manifolds without any embedding in symplectic 4-manifolds

Abstract

We show that there exist infinitely many closed 3-manifolds that do not embed in closed symplectic 4-manifolds, disproving a conjecture of Etnyre-Min-Mukherjee. To do this, we construct L-spaces that cannot bound positive or negative definite manifolds. The arguments use Heegaard Floer correction terms and instanton moduli spaces.

12 pages. Final version; to appear in Geometry & Topology

Cited by in corpus (1)

• Rational homology 3-spheres and SL(2,$\mathbb{C}$) representations