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Research shows Upsilon invariant equivalence in knot Floer homology and grid homology, suggesting key properties.
The Upsilon invariant is a concordance invariant in knot Floer homology. Földvöri [1] reconstructed the Upsilon invariant using grid homology. We prove that the Upsilon invariant in knot Floer homology and one in grid homology are equivalent. Furthermore, we show some properties of the Upsilon invariant in the framework of grid homology.
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Hajime Kubota (2026) studied this question.
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