THE MILNOR $\bar{\mu}$ INVARIANTS AND NANOPHRASES

Abstract

Two link diagrams are link homotopic if one can be transformed into the other by a sequence of Reidemeister moves and self-crossing changes. Milnor introduced invariants under link homotopy called [Formula: see text]. Nanophrases, introduced by Turaev, generalize links. In this paper, we extend the notion of link homotopy to nanophrases. We also generalize [Formula: see text] to the set of those nanophrases that correspond to virtual links.