7 papers
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…
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…
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…
On 4-dimensional 3-handle attachments
Eva Horvat, Michal Jablonowski
Kirby diagrams for smooth four-dimensional manifolds typically depict only the 1- and 2-handles, omitting the 3-handles. In this work, we investigate 3-handle attachments and provi…
Biquandle cocycle condition for invariants of immersed surface-links in the four-space
Michal Jablonowski
We consider a biquandle-cohomological framework for invariants of oriented immersed surface-links in the four-space. After reviewing projections and Roseman moves for immersed surf…
On biquandle-based invariant of immersed surface-links, Yoshikawa oriented fifth move, and ribbon 2-knots
Michal Jablonowski
We resolve an open problem by showing that the Yoshikawa's fifth oriented move in his list cannot be reproduced by any finite sequence of the other nine moves and planar isotopies.…
Rigid and shaky hard link diagrams
Michal Jablonowski
In this study of the Reidemeister moves within the classical knot theory, we focus on hard diagrams of knots and links, categorizing them as either rigid or shaky based on their ad…