Every genus one algebraically slice knot is 1-solvable
| Autor: | Davis, Christopher W., Martin, Taylor E., Otto, Carolyn, Park, JungHwan |
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| Rok vydání: | 2016 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 that for knots $\mathcal{F}_{0.5}=\mathcal{F}_1$. In particular we prove that every genus 1 algebraically slice knot is 1-solvable. Comment: 19 pages, 10 figures, to appear in Transactions of the American Mathematical Society |
| Databáze: | arXiv |
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