2019/10/14 by Jean Baptiste Meilhan, Akira Yasuhara, Meilhan, Jean-Baptiste +1
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Advanced Combinatorial Mathematics
paper · pdf · doi:10.48550/arxiv.1910.06214
Fixing two concordant links in 3--space, we study the set of all embedded concordances between them, as knotted annuli in 4--space. When regarded up to surface-concordance or link-homotopy, the set C(L) of concordances from a link L to itself forms a group. In order to investigate these groups, we define Milnor-type invariants of C(L), which are integers defined modulo a certain indeterminacy given by Milnor invariants of L. We show in particular that, for a slice link L, these invariants classify C(L) up to link-homotopy.