Unknown values in the table of knots

TL;DR

This paper compiles a regularly updated list of prime knots with minimal crossings where key invariants like unknotting number and 4-genus are unknown, aiding knot theory research.

Contribution

It introduces a dynamic, web-based table of prime knots with missing invariant data, supporting ongoing mathematical investigations.

Findings

List of prime knots with unknown invariants is systematically compiled.

The resource is integrated with KnotInfo for continuous updates.

Facilitates future research by identifying gaps in knot invariant data.

Abstract

This paper, to be regularly updated, lists those prime knots with the fewest possible number of crossings for which values of basic knot invariants, such as the unknotting number or the smooth 4-genus, are unknown. This list is being developed in conjunction with "KnotInfo" (www.indiana.edu/~knotinfo), a web-based table of knot invariants.