Heegaard floer correction terms and dedekind-rademacher sums
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 resu...
| Main Authors: | , , |
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| Format: | Journal Article |
| Language: | English |
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2014
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| Online Access: | https://hdl.handle.net/10356/106291 http://hdl.handle.net/10220/23989 |
| _version_ | 1811697694838620160 |
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| author | Jabuka, Stanislav Robins, Sinai Wang, Xinli |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Jabuka, Stanislav Robins, Sinai Wang, Xinli |
| author_sort | Jabuka, Stanislav |
| collection | NTU |
| description | 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. |
| first_indexed | 2024-10-01T07:59:20Z |
| format | Journal Article |
| id | ntu-10356/106291 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:59:20Z |
| publishDate | 2014 |
| record_format | dspace |
| spelling | ntu-10356/1062912023-02-28T19:48:55Z Heegaard floer correction terms and dedekind-rademacher sums Jabuka, Stanislav Robins, Sinai Wang, Xinli School of Physical and Mathematical Sciences DRNTU::Science::Mathematics 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. Published version 2014-10-10T06:46:39Z 2019-12-06T22:08:14Z 2014-10-10T06:46:39Z 2019-12-06T22:08:14Z 2012 2012 Journal Article Jabuka, S., Robins, S., & Wang, X. (2013). Heegaard floer correction terms and dedekind-rademacher sums. International mathematics research notices, 2013(1), 170-183. 1073-7928 https://hdl.handle.net/10356/106291 http://hdl.handle.net/10220/23989 10.1093/imrn/rnr260 en 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. 14 p. application/pdf |
| spellingShingle | DRNTU::Science::Mathematics Jabuka, Stanislav Robins, Sinai Wang, Xinli Heegaard floer correction terms and dedekind-rademacher sums |
| title | Heegaard floer correction terms and dedekind-rademacher sums |
| title_full | Heegaard floer correction terms and dedekind-rademacher sums |
| title_fullStr | Heegaard floer correction terms and dedekind-rademacher sums |
| title_full_unstemmed | Heegaard floer correction terms and dedekind-rademacher sums |
| title_short | Heegaard floer correction terms and dedekind-rademacher sums |
| title_sort | heegaard floer correction terms and dedekind rademacher sums |
| topic | DRNTU::Science::Mathematics |
| url | https://hdl.handle.net/10356/106291 http://hdl.handle.net/10220/23989 |
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