Virtual Homotopy

Details Virtual Homotopy Virtual Homotopy

2006-11-03

arxiv.org/abs/math/0611076v4

Mathematics

Geometric Topology

25 pages, 16 figures, v4. Revisions to text, added proof of skein relation

Scientific paper

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 mu and bar mu invariants to welded and virtual links. We conclude this paper with several examples, and compute the mu invariants using the Magnus expansion and Polyak's skein relation for the mu invariants.

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