The 0-concordance monoid admits an infinite linearly independent set

Dai, Irving; Miller, Maggie

doi:10.1090/proc/15311

The 0-concordance monoid admits an infinite linearly independent set
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by Irving Dai and Maggie Miller;

Proc. Amer. Math. Soc. 151 (2023), 3601-3609

DOI: https://doi.org/10.1090/proc/15311

Published electronically: April 28, 2023

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Abstract:

Under the relation of $0$-concordance, the set of knotted 2-spheres in $S^4$ forms a commutative monoid $\mathcal {M}_0$ with the operation of connected sum. Sunukjian [Int. Math. Res. Not. IMRN 17 (2015), pp. 7950–7978] has recently shown that $\mathcal {M}_0$ contains a submonoid isomorphic to $\mathbb {Z}^{\ge 0}$. In this note, we show that $\mathcal {M}_0$ contains a submonoid isomorphic to $(\mathbb {Z}^{\ge 0})^\infty$. Our argument relates the $0$-concordance monoid to linear independence of certain Seifert solids in the spin rational homology cobordism group.

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