3–Manifolds without any embedding in symplectic 4–manifolds

Daemi, Aliakbar¹ ; Lidman, Tye² ; Miller Eismeier, Mike³

¹ Department of Mathematics and Statistics, Washington University, St. Louis, MO, United States
² Department of Mathematics, North Carolina State University, Raleigh, NC, United States
³ Department of Mathematics, Columbia University, New York, NY, United States, Department of Mathematics, University of Vermont, Burlington, VT, United States

Geometry & topology, Tome 28 (2024) no. 7, pp. 3357-3372

Résumé

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.

Détail

DOI : 10.2140/gt.2024.28.3357

Keywords: $3$–manifold, definite $4$–manifold, symplectic $4$–manifolds, L–spaces, Chern–Simons invariant, instantons

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