Link concordances as surfaces in 4-space and the 4-dimensional Milnor invariants

Jean-Baptiste Meilhan (1) , Akira Yasuhara (2)

1 IF - Institut Fourier
2 Waseda University [Tokyo, Japan]

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 $\mathcal{C}(L)$ of concordances from a link $L$ to itself forms a group. In order to investigate these groups, we define Milnor-type invariants of $\mathcal{C}(L)$, 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 $\mathcal{C}(L)$ up to link-homotopy.

Domaines: Topologie géométrique [math.GT]

Jean-Baptiste Meilhan, Akira Yasuhara. Link concordances as surfaces in 4-space and the 4-dimensional Milnor invariants. Indiana University Mathematics Journal, 2019, ⟨10.1512/iumj.2022.71.9299⟩. ⟨hal-02315965⟩