Every genus one algebraically slice knot is 1-solvable

Davis, Christopher; Martin, Taylor; Otto, Carolyn; Park, JungHwan

doi:10.1090/tran/7682

Every genus one algebraically slice knot is 1-solvable
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by Christopher W. Davis, Taylor Martin, Carolyn Otto and JungHwan Park PDF

Trans. Amer. Math. Soc. 372 (2019), 3063-3082 Request permission

Abstract:

Cochran, Orr, and Teichner developed a filtration of the knot concordance group indexed by half integers called the solvable filtration. Its terms are denoted by $\mathcal {F}_n$. It has been shown that $\mathcal {F}_n/\mathcal {F}_{n.5}$ is a very large group for $n\ge 0$. For a generalization to the setting of links the third author showed that $\mathcal {F}_{n.5}/\mathcal {F}_{n+1}$ is non-trivial. In this paper we provide evidence for knots $\mathcal {F}_{0.5}=\mathcal {F}_1$. In particular we prove that every genus 1 algebraically slice knot is 1-solvable.

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