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math.GT2026
Fibred realizations of the prism quandle in the standard four-sphere
Michal Jablonowski
We study smooth fibred two-knots whose fundamental quandle is the prism quandle of order fifty-six. The candidates arise from framed circle surgery along a section of a mapping tor…
math.GT2026
Fundamental Quandles Do Not Determine the First Postnikov Invariant of 2-Knots
Michal Jablonowski
For every admissible pair of Brieskorn parameters in the Plotnick--Suciu construction, we obtain a pair of oriented -knots whose knot groups are isomorphic, whose second homotop…
math.GT2026
Unity of Jones polynomials in the unit circle and the plane
Michal Jablonowski
In this note, we study solutions of the equation for the Jones polynomial of knots and links. For the family of double-twist knots, we show that every root of unit…