{"title":"Hodge–de Rham numbers of almost complex 4-manifolds","authors":"Joana Cirici , Scott O. Wilson","doi":"10.1016/j.exmath.2022.08.005","DOIUrl":null,"url":null,"abstract":"<div><p>We introduce and study Hodge–de Rham numbers for compact almost complex 4-manifolds, generalizing the Hodge numbers of a complex surface. The main properties of these numbers in the case of complex surfaces are extended to this more general setting, and it is shown that all Hodge–de Rham numbers for compact almost complex 4-manifolds are determined by the topology, except for one (the irregularity). Finally, these numbers are shown to prohibit the existence of complex structures on certain manifolds, without reference to the classification of surfaces.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"40 4","pages":"Pages 1244-1260"},"PeriodicalIF":0.8000,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0723086922000548/pdfft?md5=955691cf023e0bdf88e05255afcf52b8&pid=1-s2.0-S0723086922000548-main.pdf","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Expositiones Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0723086922000548","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
We introduce and study Hodge–de Rham numbers for compact almost complex 4-manifolds, generalizing the Hodge numbers of a complex surface. The main properties of these numbers in the case of complex surfaces are extended to this more general setting, and it is shown that all Hodge–de Rham numbers for compact almost complex 4-manifolds are determined by the topology, except for one (the irregularity). Finally, these numbers are shown to prohibit the existence of complex structures on certain manifolds, without reference to the classification of surfaces.
引入并研究紧致几乎复4流形的Hodge - de Rham数，推广了复曲面的Hodge数。这些数在复杂曲面情况下的主要性质被推广到这种更一般的情况下，并且证明了紧致几乎复杂4流形的所有Hodge-de Rham数都是由拓扑决定的，除了一个(不规则性)。最后，这些数字被证明禁止在某些流形上存在复杂结构，而不参考表面的分类。
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