k-alternating knots

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Abstract

A projection of a knot is k-alternating if its overcrossings and undercrossings alternate in groups of k as one reads around the projection (an obvious generalization of the notion of an alternating projection). We prove that every knot admits a 2-alternating projection, which partitions nontrivial knots into two classes: alternating and 2-alternating.

MSC

57M25

Keywords

Knots
Alternating knots
Almost-alternating knots

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This research was supported by NSF grant number NSF-DMS 0243845.