The almost alternating diagrams of the trivial knot

Abstract

Bankwitz characterized an alternating diagram representing the trivial knot. A non-alternating diagram is called almost alternating if one crossing change makes the diagram alternating. We characterize an almost alternaing diagram representing the trivial knot. As a corollary we determine an unknotting number one alternating knot with a property that the unknotting operation can be done on its alternating diagram.

29 pages, 18 figures

References in corpus (1)

• Knots with unknotting number 1 and essential Conway spheres

Cited by in corpus (6)

• On closed 3-braids with unknotting number one
• Link diagrams with low Turaev genus
• On slice alternating 3-braid closures
• Unknotting numbers of diagrams of a given nontrivial knot are unbounded
• On L-space knots obtained from unknotting arcs in alternating diagrams
• Alternating Surgeries