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arXiv · 1704.04419

On intersection forms of definite 4-manifolds bounded by a rational homology 3-sphere

Dong Heon Choe·Kyungbae Park
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Abstract

We show that, if a rational homology 3-sphere $Y$ bounds a positive definite smooth 4-manifold, then there are finitely many negative definite lattices, up to the stable-equivalence, which can be realized as the intersection form of a smooth 4-manifold bounded by $Y$. To this end, we make use of constraints on definite forms bounded by $Y$ induced from Donaldson's diagonalization theorem, and correction term invariants due to Frøyshov, and Ozsváth and Szabó. In particular, we prove that all spherical 3-manifolds satisfy such finiteness property.

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Dong Heon Choe, Kyungbae Park. 2018-02-21. On intersection forms of definite 4-manifolds bounded by a rational homology 3-sphere. https://doi.org/10.1016/j.topol.2018.01.013

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