Abstract
Two welded (respectively virtual) link diagrams are homotopic if one may be transformed into the other by a sequence of extended Reidemeister moves, classical Reidemeister moves, and self crossing changes. In this paper, we extend Milnor's μ and [Formula: see text] invariants to welded and virtual links. We conclude this paper with several examples, and compute the μ invariants using the Magnus expansion and Polyak's skein relation for the μ invariants.
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