English

3-manifolds without any embedding in symplectic 4-manifolds

Geometric Topology 2024-12-04 v2 Symplectic Geometry

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.

Keywords

Cite

@article{arxiv.2207.03631,
  title  = {3-manifolds without any embedding in symplectic 4-manifolds},
  author = {Aliakbar Daemi and Tye Lidman and Mike Miller Eismeier},
  journal= {arXiv preprint arXiv:2207.03631},
  year   = {2024}
}

Comments

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