Authors produce a class of deeply slice knots in non-trivial integral homology 3-spheres by building contractible 4-manifolds where the knots are slice and verifying they fail to be slice in the 3-manifold times interval via immersed-curve Heegaard Floer invariants.
A family of $\mathfrak{sl}_{n}$-like invariants in knot Floer homology
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abstract
We define and study a family of link invariants $\mathit{HFK}_{n}(L)$. Although these homology theories are defined using holomorphic disc counts, they share many properties with $sl_{n}$ homology. Using these theories, we give a framework that generalizes the conjectured spectral sequence from Khovanov homology to $\delta$-graded knot Floer homology. In particular, we conjecture that for all links $L$ in $S^3$ and all $n\ge 1$, there is a spectral sequence from the $sl_{n}$ homology of $L$ to $\mathit{HFK}_{n}(L)$.
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math.GT 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Deeply Slice Knot Detection via Immersed Curves
Authors produce a class of deeply slice knots in non-trivial integral homology 3-spheres by building contractible 4-manifolds where the knots are slice and verifying they fail to be slice in the 3-manifold times interval via immersed-curve Heegaard Floer invariants.