Singular instanton Floer homology produces exotic pairs of slice disks for a strongly invertible Z-slice knot whose symmetric disks stay exotic under stabilizations by definite 4-manifolds or projective planes.
On 2-knots and connected sums with projective planes
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abstract
In this paper, we generalize a result of Satoh to show that for any odd natural $n$, the connected sum of the $n$-twist spun sphere of a knot $K$ and an unknotted projective plane in the 4-sphere is equivalent to the same unknotted projective plane. We additionally provide a fix to a small error in Satoh's proof of the case that $K$ is a 2-bridge knot.
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2026 1verdicts
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Exotic disks and singular instanton Floer homology
Singular instanton Floer homology produces exotic pairs of slice disks for a strongly invertible Z-slice knot whose symmetric disks stay exotic under stabilizations by definite 4-manifolds or projective planes.