2020/05/11 by James Conant, Conant, James, Rob Schneiderman +3
Mathematics · #57M25 #57M27 #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2005.05381
openalex publication_date 2020/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that for each k∈ℕ, a link L⊂ S3 bounds a degree k Whitney tower in the 4-ball if and only if it is Ck-concordant to the unlink. This means that L is obtained from the unlink by a finite sequence of concordances and degree k clasper surgeries. In our construction the trees associated to the Whitney towers coincide with the trees associated to the claspers. As a corollary to our previous obstruction theory for Whitney towers in the 4-ball, it follows that the Ck-concordance filtration of links is classified in terms of Milnor invariants, higher-order Sato-Levine and Arf invariants. Using a new notion of k-repeating twisted Whitney towers, we also classify a natural generalization of the notion of link homotopy, called twisted self Ck-concordance, in terms of k-repeating Milnor invariants and k-repeating Arf invariants.