{"title":"A characterization of heaviness in terms of relative symplectic cohomology","authors":"Cheuk Yu Mak, Yuhan Sun, Umut Varolgunes","doi":"10.1112/topo.12327","DOIUrl":null,"url":null,"abstract":"<p>For a compact subset <math>\n <semantics>\n <mi>K</mi>\n <annotation>$K$</annotation>\n </semantics></math> of a closed symplectic manifold <math>\n <semantics>\n <mrow>\n <mo>(</mo>\n <mi>M</mi>\n <mo>,</mo>\n <mi>ω</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$(M, \\omega)$</annotation>\n </semantics></math>, we prove that <math>\n <semantics>\n <mi>K</mi>\n <annotation>$K$</annotation>\n </semantics></math> is heavy if and only if its relative symplectic cohomology over the Novikov field is nonzero. As an application, we show that if two compact sets are not heavy and Poisson commuting, then their union is also not heavy. A discussion on superheaviness together with some partial results is also included.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"17 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.12327","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Topology","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/topo.12327","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
For a compact subset of a closed symplectic manifold , we prove that is heavy if and only if its relative symplectic cohomology over the Novikov field is nonzero. As an application, we show that if two compact sets are not heavy and Poisson commuting, then their union is also not heavy. A discussion on superheaviness together with some partial results is also included.
期刊介绍：
The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal.
The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.
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