Year: 2026
Type: preprint
Abstract: 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 torus, using the two possible normal-framing classes. We prove that both ambient homotopy four-spheres are diffeomorphic to the standard four-sphere. The candidates have the same knot group and diffeomorphic exteriors, but they are inequivalent even as topological pairs. Every smooth fibred realization of this quandle in a homotopy four-sphere is equivalent, up to knot orientation, to exactly one of these two knots. Standardness follows from a Whitehead-link model for the orbit orbifold together with circle-action recognition. Inequivalence is detected by the third cyclic branched covers, on which a spin-bordism secondary invariant takes different values. Thus the parameter-seven prism quandle admits smooth fibred realizations in the standard four-sphere.
Source: arXiv (Cornell University)
Author: Jablonowski, Michal
Institution: University of Gdańsk
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214292586