Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Every genus one algebraically slice knot is 1-solvable   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.

11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org