Title

Genus Ranges of Chord Diagrams

Document Type

Article

Publication Date

2015

Keywords

Chord diagrams, genus ranges, double-occurrence words

Digital Object Identifier (DOI)

https://doi.org/10.1142/S0218216515500224

Abstract

A chord diagram consists of a circle, called the backbone, with line segments, called chords, whose endpoints are attached to distinct points on the circle. The genus of a chord diagram is the genus of the orientable surface obtained by thickening the backbone to an annulus and attaching bands to the inner boundary circle at the ends of each chord. Variations of this construction are considered here, where bands are possibly attached to the outer boundary circle of the annulus. The genus range of a chord diagram is the genus values over all such variations of surfaces thus obtained from a given chord diagram. Genus ranges of chord diagrams for a fixed number of chords are studied. Integer intervals that can be, and those that cannot be, realized as genus ranges are investigated. Computer calculations are presented, and play a key role in discovering and proving the properties of genus ranges.

Was this content written or created while at USF?

Yes

Citation / Publisher Attribution

Journal of Knot Theory and Its Ramifications, v. 24, issue 4, art. 1550022

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