Heegaard floer correction terms and dedekind-rademacher sums
Date of Issue2012
School of Physical and Mathematical Sciences
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.
International mathematics research notices
© 2012 The Author(s). This paper was published in International Mathematics Research Notices and is made available as an electronic reprint (preprint) with permission of the Author(s). The paper can be found at the following official DOI: http://dx.doi.org/10.1093/imrn/rnr260. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.