Finiteness of mock-alternating virtual links with fixed mock-determinant

Determine whether only finitely many mock-alternating virtual links have any given mock-determinant.

Background

The paper introduces mock-alternating virtual links recursively using the mock-determinant, defined as the L1-norm of the Jones-Kauffman polynomial evaluated at an eighth root of unity. The class is shown to have alternating Jones-Kauffman polynomials, and a twisting construction produces infinite families of mock-alternating virtual links from suitable examples.

Despite this construction, the paper does not resolve whether fixing the numerical value of the mock-determinant still permits only finitely many mock-alternating virtual links. The question is explicitly motivated by finiteness conjectures concerning quasi-alternating links.