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math.GT2025
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…
math.GT2025
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…
math.GT2025
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.…