Mod 2 instanton homology and 4-manifolds with boundary

Kim A. Frøyshov

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arXiv · 2307.03950

Mod 2 instanton homology and 4-manifolds with boundary

Kim A. Frøyshov

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Abstract

Using instanton homology with coefficients in $Z/2$ we construct a homomorphism $q_2$ from the homology cobordism group in dimension 3 to the integers which is not a rational linear combination of the instanton $h$--invariant and the Heegaard Floer correction term $d$. If an oriented homology $3$--sphere $Y$ bounds a smooth, compact, negative definite $4$--manifold without $2$--torsion in its homology then $q_2(Y)\ge0$, with strict inequality if the intersection form is non-standard.

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BibTeX RIS

Kim A. Frøyshov. 2023-07-08. Mod 2 instanton homology and 4-manifolds with boundary. https://arxiv.org/abs/2307.03950

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