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VIRTUAL HOMOTOPY

McKendree University, 701 College Road, Lebanon, Illinois 62254, USA

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Department of Mathematics, Statistics, & Computer Science, University of Illinois at Chicago, 851 South Morgan St, Chicago, IL 60607-7045, USA

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https://doi.org/10.1142/S0218216510008200Cited by:6 (Source: Crossref)

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 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.

Keywords:

AMSC: 57M27

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Vol. 19, No. 07

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Accepted 16 April 2009

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VIRTUAL HOMOTOPY

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