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Two Heegaard Floer knot complexes are called stably equivalent if an acycliccomplex can be added to each complex to make them filtered chain homotopyequivalent. Hom showed that if two knots are concordant, then their knotcomplexes are stably equivalent. Invariants of stable equivalence include theconcordance invariants $\tau$, $\varepsilon$, and $\Upsilon$. Feller andKrcatovich gave a relationship between the Upsilon invariants of torus knots.We use secondary Upsilon invariants defined by Kim and Livingston to show thatthese relations do not extend to stable equivalence.

Using secondary Upsilon invariants to rule out stable equivalence of knot complexes