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Z -disks in C P²

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Analysis of z-disks bounded by knots shows bijection with unitary units in a specific ring, indicating new invariants.

A bijection exists between rel. boundary isotopy classes of z-disks and a quotient of unitary units.
The homology class of a loop in S^3 K captures complete invariants of the disk configurations.
Knot K can bound infinitely many distinct z-disks with the same fundamental group, as shown through examples.
Number-theoretic insights lead to bounds on knots with quadratic Alexander polynomials affecting z-disk existence.

Conway et al. (2025) studied this question.

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