{"title":"全等覆盖中 k 维收缩的增长","authors":"Mikhail Belolipetsky, Shmuel Weinberger","doi":"10.1007/s00039-024-00686-7","DOIUrl":null,"url":null,"abstract":"<p>We study growth of absolute and homological <i>k</i>-dimensional systoles of arithmetic <i>n</i>-manifolds along congruence coverings. Our main interest is in the growth of systoles of manifolds whose real rank <i>r</i>≥2. We observe, in particular, that in some cases for <i>k</i>=<i>r</i> the growth function tends to oscillate between a power of a logarithm and a power function of the degree of the covering. This is a new phenomenon. We also prove the expected polylogarithmic and constant power bounds for small and large <i>k</i>, respectively.</p>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Growth of k-Dimensional Systoles in Congruence Coverings\",\"authors\":\"Mikhail Belolipetsky, Shmuel Weinberger\",\"doi\":\"10.1007/s00039-024-00686-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We study growth of absolute and homological <i>k</i>-dimensional systoles of arithmetic <i>n</i>-manifolds along congruence coverings. Our main interest is in the growth of systoles of manifolds whose real rank <i>r</i>≥2. We observe, in particular, that in some cases for <i>k</i>=<i>r</i> the growth function tends to oscillate between a power of a logarithm and a power function of the degree of the covering. This is a new phenomenon. We also prove the expected polylogarithmic and constant power bounds for small and large <i>k</i>, respectively.</p>\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-06-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00039-024-00686-7\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00039-024-00686-7","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 0
摘要
我们研究算术 n 维流形的绝对和同调 k 维系统沿全等覆盖的增长。我们的主要兴趣在于实阶 r≥2 的流形的增量。我们特别观察到，在 k=r 的某些情况下，增长函数趋向于在对数的幂函数和覆盖度的幂函数之间摇摆。这是一个新现象。我们还分别证明了小 k 和大 k 的预期多对数和常数幂边界。
Growth of k-Dimensional Systoles in Congruence Coverings
We study growth of absolute and homological k-dimensional systoles of arithmetic n-manifolds along congruence coverings. Our main interest is in the growth of systoles of manifolds whose real rank r≥2. We observe, in particular, that in some cases for k=r the growth function tends to oscillate between a power of a logarithm and a power function of the degree of the covering. This is a new phenomenon. We also prove the expected polylogarithmic and constant power bounds for small and large k, respectively.
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