3-manifolds without any embedding in symplectic 4-manifolds

Aliakbar Daemi; Tye Lidman; Mike Miller Eismeier

doi:10.2140/gt.2024.28.3357

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arXiv · 2207.03631

3-manifolds without any embedding in symplectic 4-manifolds

Aliakbar Daemi·Tye Lidman·Mike Miller Eismeier

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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.

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Aliakbar Daemi, Tye Lidman, Mike Miller Eismeier. 2022-07-08. 3-manifolds without any embedding in symplectic 4-manifolds. https://doi.org/10.2140/gt.2024.28.3357

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