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- Title
Band-passes and long virtual knot concordance.
- Authors
Chrisman, Micah
- Abstract
Every classical knot is band-pass equivalent to the unknot or the trefoil. The band-pass class of a knot is a concordance invariant. Every ribbon knot, for example, is band-pass equivalent to the unknot. Here we introduce the long virtual knot concordance group . It is shown that for every concordance class , there is a that is not band-pass equivalent to and an that is not band-pass equivalent to either the long unknot or any long trefoil. This is accomplished by proving that is a band-pass invariant but not a concordance invariant of long virtual knots, where and generate the degree two Polyak group for long virtual knots.
- Subjects
KNOT groups; CONCORDANCES (Topology); INVARIANTS (Mathematics); TOPOLOGICAL degree; TREFOIL knots
- Publication
Journal of Knot Theory & Its Ramifications, 2017, Vol 26, Issue 10, p-1
- ISSN
0218-2165
- Publication type
Article
- DOI
10.1142/S0218216517500572