Hyperbolic manifolds with a large number of systoles

IF 1.2 2区数学 Q1 MATHEMATICS

Transactions of the American Mathematical Society Pub Date : 2023-10-11 DOI:10.1090/tran/9049

Cayo Dória, Emanoel Freire, Plinio Murillo

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These results generalize previous work of Schmutz for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n equals 2\"> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">n=2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and Dória-Murillo for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n equals 3\"> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">n=3</mml:annotation> </mml:semantics> </mml:math> </inline-formula> to higher dimensions.","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions of the American Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/tran/9049","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

Abstract

In this article, for any n ≥ 4 n\geq 4 we construct a sequence of compact hyperbolic n n -manifolds { M i } \{M_i\} with number of systoles at least as v o l ( M i ) 1 + 1 3 n ( n + 1 ) − ϵ \mathrm {vol}(M_i)^{1+\frac {1}{3n(n+1)}-\epsilon } for any ϵ > 0 \epsilon >0 . In dimension 3, the bound is improved to v o l ( M i ) 4 3 − ϵ \mathrm {vol}(M_i)^{\frac {4}{3}-\epsilon } . These results generalize previous work of Schmutz for n = 2 n=2 , and Dória-Murillo for n = 3 n=3 to higher dimensions.

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具有大量收缩的双曲流形

在这个文章,对于任何n≥4 \ geq 4我们构造a序列的紧凑型轿车hyperbolic n n -manifolds {M i} {M_i \}用systoles至少美国的当家v o l (M) 1 + 1 3 n (n + 1)−ϵ\ mathrm{卷}(M_i) ^ {1 + \ frac {1} {3n (n + 1)} - \ epsilon} for任何ϵ>0 \epsilon > 0。在第三维度,被束缚的是改良到v o l (M) 4 3−ϵ\ mathrm{卷}(M_i) ^ {\ frac {4} {3} - epsilon的。这些重复一般用于n=2 =2的Schmutz工作，而Doria-Murillo为n=3 =3，以达到更高的维度。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Transactions of the American Mathematical Society 数学-数学

CiteScore

2.30

自引率

7.70%

发文量

171

审稿时长

3-6 weeks

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