Heegaard floer correction terms and dedekind-rademacher sums

Abstract

We derive a closed formula for the Heegaard Floer correction terms of lens spaces in terms of the classical Dedekind sum and its generalization, the Dedekind–Rademacher sum. Our proof relies on a reciprocity formula for the correction terms established by Ozsváth and Szabó. A consequence of our result is that the Casson–Walker invariant of a lens space equals the average of its Heegaard Floer correction terms. Additionally, we find an obstruction for the equality and equality with opposite sign, of two correction terms of the same lens space. Using this obstruction we are able to derive an optimal upper bound on the number of vanishing correction terms of lens spaces with square order second cohomology.