Evaluations of Link Polynomials and Recent Constructions in Heegaard Floer Theory

Using a definition of Euler characteristic for fractionally graded complexes based on roots of unity, we show that the Euler characteristics of Dowlin's "sl(n)-like" Heegaard Floer knot invariants HFKn recover both Alexander polynomial evaluations and sl(n) polynomial evaluations at certain roots of unity for links in S3. We show that the equality of these evaluations can be viewed as the decategorified content of the conjectured spectral sequences relating sl(n) homology and HFKn.