EVERY GENUS ONE ALGEBRAICALLY SLICE KNOT IS 1-SOLVABLE

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 F-n. It has been shown that F-n/F-n.5 is a very large group for n >= 0. For a generalization to the setting of links the third author showed that F-n.5/Fn+1 is non-trivial. In this paper we provide evidence for knots F-0.5 = F-1. In particular we prove that every genus 1 algebraically slice knot is 1-solvable.