Instantons, indefinite 4-manifolds, and Dehn surgery

Aliakbar Daemi; Xingpei Liu; Mike Miller Eismeier

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arXiv · 2608.27904

Instantons, indefinite 4-manifolds, and Dehn surgery

Aliakbar Daemi·Xingpei Liu·Mike Miller Eismeier

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Abstract

We prove that there exist hyperbolic integer homology spheres with arbitrarily large Dehn surgery number. Previously, no integer homology sphere was known to have a surgery number larger than $2$. Our approach uses Froyshov's invariant $q_3$ of integer homology spheres, which is defined in terms of mod 2 instanton homology. We show that if $W: Y \to Y'$ is a cobordism between integer homology spheres with no $2$-torsion in its first homology, then $-b^+(W) \le q_3(Y') - q_3(Y) \le b^-(W)$. We also extend both $q_3$ and the inequality to rational homology spheres.

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BibTeX RIS

Aliakbar Daemi, Xingpei Liu, Mike Miller Eismeier. 2026-08-28. Instantons, indefinite 4-manifolds, and Dehn surgery. https://arxiv.org/abs/2608.27904

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