{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:50:50Z","timestamp":1740124250422,"version":"3.37.3"},"reference-count":16,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2024,6,19]],"date-time":"2024-06-19T00:00:00Z","timestamp":1718755200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,6,19]],"date-time":"2024-06-19T00:00:00Z","timestamp":1718755200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100009934","name":"E\u00f6tv\u00f6s Lor\u00e1nd University","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100009934","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Period Math Hung"],"published-print":{"date-parts":[[2024,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper we consider the (topological) lattice cohomology <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathbb {H}^*$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mrow>\n                      <mml:mi>H<\/mml:mi>\n                    <\/mml:mrow>\n                    <mml:mo>\u2217<\/mml:mo>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> of a surface singularity with rational homology sphere link. In particular, we will be studying two sets of (topological) invariants related to it: the weight function <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\upchi $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03c7<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> that induces the cohomology and the topological subspace arrangement <jats:inline-formula><jats:alternatives><jats:tex-math>$$T(\\ell ,I)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>T<\/mml:mi>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mi>\u2113<\/mml:mi>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mi>I<\/mml:mi>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> at each lattice point <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\ell $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u2113<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> \u2014 the latter of which is the weaker of the two. We shall prove that the two are in fact equivalent by establishing an algorithm to compute <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\upchi $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03c7<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> from the subspace arrangement. Replacing the topological arrangements with the analytic, we get another formula \u2014 one that connects them with the analytic lattice cohomology introduced and studied in our earlier papers. In fact, this connection served as the original motivation for the definition of the latter. Aside from the historical interest, this parallel also provides us with tools to study more easily the connection between the two cohomologies.<\/jats:p>","DOI":"10.1007\/s10998-024-00590-5","type":"journal-article","created":{"date-parts":[[2024,6,19]],"date-time":"2024-06-19T13:04:42Z","timestamp":1718802282000},"page":"298-312","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Lattice cohomology and subspace arrangements: the topological and analytic cases"],"prefix":"10.1007","volume":"89","author":[{"given":"Tam\u00e1s","family":"\u00c1goston","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,6,19]]},"reference":[{"key":"590_CR1","unstructured":"T. \u00c1goston, A. N\u00e9methi, The analytic lattice cohomology of surface singularities, (2021), arXiv:2108.12294 [math.AG]"},{"key":"590_CR2","unstructured":"T. \u00c1goston, A. N\u00e9methi, Analytic lattice cohomology of surface singularities, II (the equivariant case), (2021), arXiv:2108.12429 [math.AG]"},{"key":"590_CR3","unstructured":"T. \u00c1goston, A. N\u00e9methi, The analytic lattice cohomology of isolated singularities, (2021), arXiv:2109.11266 [math.AG]"},{"key":"590_CR4","unstructured":"T. \u00c1goston, A. N\u00e9methi, Analytic lattice cohomology of isolated curve singularities, (2021), arXiv:2301.08981 [math.AG]"},{"issue":"6","key":"590_CR5","doi-asserted-by":"publisher","first-page":"1115","DOI":"10.1017\/S1474748017000329","volume":"18","author":"I Dai","year":"2019","unstructured":"I. Dai, C. Manolescu, Involutive Heegaard Floer homology and plumbed three-manifolds. J. Inst. Math. Jussieu 18(6), 1115\u20131155 (2019)","journal-title":"J. Inst. Math. Jussieu"},{"issue":"4","key":"590_CR6","doi-asserted-by":"publisher","first-page":"2219","DOI":"10.2140\/gt.2016.20.2219","volume":"20","author":"J Hom","year":"2016","unstructured":"J. Hom, C. Karakurt, T. Lidman, Surgery obstructions and Heegaard Floer homology. Geom. Topol. 20(4), 2219\u20132251 (2016)","journal-title":"Geom. Topol."},{"issue":"10","key":"590_CR7","doi-asserted-by":"publisher","first-page":"7291","DOI":"10.1090\/S0002-9947-2014-06451-9","volume":"367","author":"\u00c7 Karakurt","year":"2015","unstructured":"\u00c7. Karakurt, T. Lidman, Rank inequalities for the Heegaard Floer homology of Seifert homology spheres. Transactions of the Amer. Math. Soc. 367(10), 7291\u20137322 (2015)","journal-title":"Transactions of the Amer. Math. Soc."},{"issue":"3","key":"590_CR8","doi-asserted-by":"publisher","first-page":"1850019","DOI":"10.1142\/S0129167X18500192","volume":"29","author":"\u00c7 Karakurt","year":"2018","unstructured":"\u00c7. Karakurt, F. Ozturk, Contact Structures on AR-singularity links. Internat. J. Math. 29(3), 1850019 (2018)","journal-title":"Internat. J. Math."},{"issue":"11","key":"590_CR9","doi-asserted-by":"publisher","first-page":"2938","DOI":"10.1093\/imrn\/rnu015","volume":"2015","author":"T L\u00e1szl\u00f3","year":"2015","unstructured":"T. L\u00e1szl\u00f3, A. N\u00e9methi, Reduction theorem for lattice cohomology. Int. Math. Research Notices 2015(11), 2938\u20132985 (2015)","journal-title":"Int. Math. Research Notices"},{"issue":"2","key":"590_CR10","doi-asserted-by":"publisher","first-page":"991","DOI":"10.2140\/gt.2005.9.991","volume":"9","author":"A N\u00e9methi","year":"2005","unstructured":"A. N\u00e9methi, On the Ozsv\u00e1th-Szab\u00f3 invariant of negative definite plumbed 3-manifolds. Geom. Topol. 9(2), 991\u20131042 (2005)","journal-title":"Geom. Topol."},{"key":"590_CR11","doi-asserted-by":"crossref","unstructured":"A. N\u00e9methi, Graded roots and singularities. In: J.-P. Brasselet, J.N. Damon, D.T. L\u00ea, M. Oka (ed.): Singularities in Geometry and Topology (p. 394\u2013463), World Scientific (2007)","DOI":"10.1142\/9789812706812_0013"},{"issue":"2","key":"590_CR12","doi-asserted-by":"publisher","first-page":"507","DOI":"10.2977\/prims\/1210167336","volume":"44","author":"A N\u00e9methi","year":"2008","unstructured":"A. N\u00e9methi, Lattice cohomology of normal surface singularities. Publ. of the Res. Inst. for Math. Sci. 44(2), 507\u2013543 (2008)","journal-title":"Publ. of the Res. Inst. for Math. Sci."},{"issue":"4","key":"590_CR13","doi-asserted-by":"publisher","first-page":"959","DOI":"10.4171\/jems\/272","volume":"13","author":"A N\u00e9methi","year":"2011","unstructured":"A. N\u00e9methi, The Seiberg-Witten invariants of negative definite plumbed 3-manifolds. J. Eur. Math. Soc. 13(4), 959\u2013974 (2011)","journal-title":"J. Eur. Math. Soc."},{"key":"590_CR14","doi-asserted-by":"crossref","unstructured":"A. N\u00e9methi, Normal surface singularities (Ergebnisse der Math. und ihrer Grenzgebiete 74), Springer, (2022)","DOI":"10.1007\/978-3-031-06753-2"},{"key":"590_CR15","volume-title":"Elements of Homotopy Theory","author":"GW Whitehead","year":"1995","unstructured":"G.W. Whitehead, Elements of Homotopy Theory (Springer, Cham, 1995)"},{"key":"590_CR16","unstructured":"I. Zemke, The equivalence of lattice and Heegaard Floer homology, (2021), arXiv:2111.14962 [math.GT]"}],"container-title":["Periodica Mathematica Hungarica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-024-00590-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10998-024-00590-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-024-00590-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,16]],"date-time":"2024-12-16T11:08:17Z","timestamp":1734347297000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10998-024-00590-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,19]]},"references-count":16,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,12]]}},"alternative-id":["590"],"URL":"https:\/\/doi.org\/10.1007\/s10998-024-00590-5","relation":{},"ISSN":["0031-5303","1588-2829"],"issn-type":[{"type":"print","value":"0031-5303"},{"type":"electronic","value":"1588-2829"}],"subject":[],"published":{"date-parts":[[2024,6,19]]},"assertion":[{"value":"16 September 2023","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 June 2024","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}