The n-solvable filtration of the m-component smooth (string) link
concordance group, β―βFn+1mββFn.5mββFnmββ―βF1mββF0.5mββF0mββFβ0.5mββCm, as defined by Cochran, Orr, and
Teichner, is a tool for studying smooth knot and link concordance that yields
important results in low-dimensional topology. The focus of this paper is to
give a characterization of the set of 0-solvable links. We introduce a new
equivalence relation on links called 0-solve equivalence and establish both an
algebraic and a geometric classification of L0mβ, the set of links
up to 0-solve equivalence. We show that L0mβ has a group structure
isomorphic to the quotient Fβ0.5β/F0β of concordance
classes of string links and classify this group, showing that L0mββ Fβ0.5mβ/F0mββ Z2mββZ(3mβ)βZ2(2mβ)β. Finally, using
results of Conant, Schneiderman, and Teichner, we show that 0-solvable links
are precisely the links that bound class 2 gropes and support order 2 Whitney
towers in the 4-ball.Comment: 34 page