Research ArticleNo Access

Some generalizations of Satoh’s Tube map

Medaille University, Buffalo, New York, USA

https://doi.org/10.1142/S0218216522500468Cited by:0 (Source: Crossref)

Abstract

Satoh defined a map from virtual links to ribbon surfaces embedded in $S^{4}$ $S^{4}$ . Herein, we generalize this map to virtual $m$ $m$ -links, and use this to construct generalizations of welded and extended welded knots to higher dimensions. This also allows us to construct two new geometric pictures of virtual $m$ $m$ -links, including 1-links.

Keywords:

AMSC: 57K10, 57R40

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