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On the Upsilon invariant in grid homology | Synapse

March 23, 2026

On the Upsilon invariant in grid homology

Puntos clave

The objective is to prove the equivalence of the Upsilon invariant in knot Floer homology and grid homology.
Detailed examination of knot Floer homology and grid homology frameworks.
Comparison of the Upsilon invariants in both contexts.
Analysis of properties related to the Upsilon invariant.
Demonstrated that the Upsilon invariant in both homologies is equivalent.
Outlined specific properties of the Upsilon invariant within grid homology context.

Resumen

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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Cite This Study

Hajime Kubota (Fri,) studied this question.

synapsesocial.com/papers/69c08b6ba48f6b84677f8a13 https://doi.org/https://doi.org/10.1142/s0218216526500276

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