Homological instability for moduli spaces of smooth 4-manifolds

Hokuto Konno; Jianfeng Lin

doi:10.2140/gt.2026.30.2993

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arXiv · 2211.03043

Homological instability for moduli spaces of smooth 4-manifolds

Hokuto Konno·Jianfeng Lin

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Abstract

We prove that homological stability fails for the moduli space of any simply-connected closed smooth 4-manifold in any degree of homology, unlike what happens in all dimensions $\neq 4$. We detect also the homological discrepancy between various moduli spaces, such as topological and smooth moduli spaces of 4-manifolds, and moduli spaces of 4-manifolds with positive scalar curvature metrics. To prove these results, we use the Seiberg-Witten equations to construct a new characteristic class of families of 4-manifolds, which is unstable and detects the difference between the smooth and topological categories in dimension 4.

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BibTeX RIS

Hokuto Konno, Jianfeng Lin. 2022-11-06. Homological instability for moduli spaces of smooth 4-manifolds. https://doi.org/10.2140/gt.2026.30.2993

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