Concordance for framed and twisted virtual knots

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Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Gaudreau, Robin

Formal Metadata

Title

Concordance for framed and twisted virtual knots

Title of Series

Unifying 4-Dimensional Knot Theory (19w5118)

Number of Parts

Author

Gaudreau, Robin

License

CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.

Identifiers

10.5446/57643 (DOI)

Publisher

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Release Date

2019

Language

English

Content Metadata

Subject Area

Life Sciences Mathematics Physics

Genre

Workshop/Interactive Format Lecture

Abstract

For smooth knots in the 3 sphere, concordance has a purely geometrical definition as the equivalence generated by genus 0 cobordisms in the sphere times an interval. For virtual knots, the relation is extended by using diagram-based definitions. Both framed and twisted virtual knots have a rigidity imbued by a choice of unit normal vector field to the knot. This talk presents combinatorial definitions for concordance of framed and twisted virtual knots and slice obstructions coming from self-linking numbers.