On codimension two embeddings up to link‐homotopy
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DOI: 10.1112/topo.12041
Abstract: We consider knotted annuli in 4–space, called 2–string-links, which are knotted surfaces in codi-mension two that are naturally related, via closure operations, to both 2–links and 2–torus links. We classify 2–string-links up to link-homotopy by… read more here.
Keywords: string links; codimension two; link homotopy; two embeddings ... See more keywords
Detecting Whitney disks for link maps in the four-sphere
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DOI: 10.1142/s0218216517500778
Abstract: It is an open problem whether Kirk’s σ-invariant is the complete obstruction to a link map f : S+2 ∪ S −2 → S4 being link homotopic to the trivial link. The link homotopy invariant… read more here.
Keywords: whitney disks; link; link homotopy; link map ... See more keywords
Quasi-trivial quandles and biquandles, cocycle enhancements and link-homotopy of pretzel links
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DOI: 10.1142/s0218216518430071
Abstract: We investigate some algebraic structures called quasi-trivial quandles and we use them to study link-homotopy of pretzel links. Precisely, a necessary and sufficient condition for a pretzel link with at least two components being trivial… read more here.
Keywords: homotopy pretzel; trivial quandles; link homotopy; quasi trivial ... See more keywords