3–Manifolds without any embedding in symplectic 4–manifolds

Aliakbar Daemi; Tye Lidman; Mike Miller Eismeier

doi:10.2140/gt.2024.28.3357

3–Manifolds without any embedding in symplectic 4–manifolds

Aliakbar Daemi
, Tye Lidman
, Mike Miller Eismeier

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	3357-3372
Number of pages	16
Journal	Geometry and Topology
Volume	28
Issue number	7
DOIs	https://doi.org/10.2140/gt.2024.28.3357
State	Published - 2024

Keywords

3–manifold
Chern–Simons invariant
L–spaces
definite 4–manifold
instantons
symplectic 4–manifolds

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10.2140/gt.2024.28.3357

Cite this

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title = "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.",

keywords = "3–manifold, Chern–Simons invariant, L–spaces, definite 4–manifold, instantons, symplectic 4–manifolds",

author = "Aliakbar Daemi and Tye Lidman and Eismeier, \{Mike Miller\}",

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language = "English",

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T1 - 3–Manifolds without any embedding in symplectic 4–manifolds

AU - Daemi, Aliakbar

AU - Lidman, Tye

AU - Eismeier, Mike Miller

PY - 2024

Y1 - 2024

N2 - 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.

AB - 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.

KW - 3–manifold

KW - Chern–Simons invariant

KW - L–spaces

KW - definite 4–manifold

KW - instantons

KW - symplectic 4–manifolds

UR - https://www.scopus.com/pages/publications/85211467858

U2 - 10.2140/gt.2024.28.3357

DO - 10.2140/gt.2024.28.3357

M3 - Article

AN - SCOPUS:85211467858

SN - 1465-3060

VL - 28

SP - 3357

EP - 3372

JO - Geometry and Topology

JF - Geometry and Topology

IS - 7

ER -

3–Manifolds without any embedding in symplectic 4–manifolds

Abstract

Keywords

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