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Topological mixing of positive diagonal flows 正对角流动的拓扑混合
2区 数学
Israel Journal of Mathematics Pub Date : 2023-11-13 DOI: 10.1007/s11856-023-2561-1
Nguyen-Thi Dang
{"title":"Topological mixing of positive diagonal flows","authors":"Nguyen-Thi Dang","doi":"10.1007/s11856-023-2561-1","DOIUrl":"https://doi.org/10.1007/s11856-023-2561-1","url":null,"abstract":"Let $G$ be a semi-simple real Lie group without compact factors and $ Gamma < G$ a Zariski dense, discrete subgroup. We study the topological dynamics of positive diagonal flows on $Gamma backslash G$. We extend Hopf coordinates to Bruhat-Hopf coordinates of $G$, which gives the framework to estimate the elliptic part of products of large generic loxodromic elements. By rewriting results of Guivarc'h-Raugi into Bruhat-Hopf coordinates, we partition the preimage in $Gamma backslash G$ of the non-wandering set of mixing regular Weyl chamber flows, into finitely many dynamically conjugated subsets. We prove a necessary condition for topological mixing, and when the connected component of the identity of the centralizer of the Cartan subgroup is abelian, we prove it is sufficient.","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134993194","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
The high-dimensional cohomology of the moduli space of curves with level structures II: punctures and boundary 具有水平结构曲线模空间的高维上同调II:点与边界
2区 数学
Israel Journal of Mathematics Pub Date : 2023-11-13 DOI: 10.1007/s11856-023-2566-9
Tara Brendle, Nathan Broaddus, Andrew Putman
{"title":"The high-dimensional cohomology of the moduli space of curves with level structures II: punctures and boundary","authors":"Tara Brendle, Nathan Broaddus, Andrew Putman","doi":"10.1007/s11856-023-2566-9","DOIUrl":"https://doi.org/10.1007/s11856-023-2566-9","url":null,"abstract":"","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134993189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
Regularity results for local solutions to some anisotropic elliptic equations 一些各向异性椭圆方程局部解的正则性结果
2区 数学
Israel Journal of Mathematics Pub Date : 2023-11-13 DOI: 10.1007/s11856-023-2564-y
Giuseppina di Blasio, Filomena Feo, Gabriella Zecca
{"title":"Regularity results for local solutions to some anisotropic elliptic equations","authors":"Giuseppina di Blasio, Filomena Feo, Gabriella Zecca","doi":"10.1007/s11856-023-2564-y","DOIUrl":"https://doi.org/10.1007/s11856-023-2564-y","url":null,"abstract":"Abstract In this paper we study the higher integrability of local solutions for a class of anisotropic equations with lower order terms whose growth coefficients lay in Marcinkiewicz spaces. A condition for the boundedness of such solutions is also given.","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134993193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Many forcing axioms for all regular uncountable cardinals 许多强制公理适用于所有正则不可数基数
2区 数学
Israel Journal of Mathematics Pub Date : 2023-11-13 DOI: 10.1007/s11856-023-2570-0
Noam Greenberg, Saharon Shelah
{"title":"Many forcing axioms for all regular uncountable cardinals","authors":"Noam Greenberg, Saharon Shelah","doi":"10.1007/s11856-023-2570-0","DOIUrl":"https://doi.org/10.1007/s11856-023-2570-0","url":null,"abstract":"Abstract A central theme in set theory is to find universes with extreme, well-understood behaviour. The case we are interested in is assuming GCH and having a strong forcing axiom of higher order than usual. Instead of “every suitable forcing notion of size λ has a sufficiently generic filter” we shall say “for every suitable method of producing notions of forcing based on a given stationary set, there is such a suitable stationary set S and sufficiently generic filters for the notion of forcing attached to S ”. Such notions of forcing are important for Abelian group theory, but this application is delayed for a sequel.","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134993167","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Martin–Löf reducibility and cost functions Martin-Löf可约性和成本函数
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2023-11-13 DOI: 10.1007/s11856-023-2565-x
Noam Greenberg, Joseph S. Miller, André Nies, Dan Turetsky
{"title":"Martin–Löf reducibility and cost functions","authors":"Noam Greenberg, Joseph S. Miller, André Nies, Dan Turetsky","doi":"10.1007/s11856-023-2565-x","DOIUrl":"https://doi.org/10.1007/s11856-023-2565-x","url":null,"abstract":"<p>Martin—Löf (ML)-reducibility compares the complexity of <i>K</i>-trivial sets of natural numbers by examining the Martin—Löf random sequences that compute them. One says that a <i>K</i>-trivial set <i>A</i> is ML-reducible to a <i>K</i>-trivial set <i>B</i> if every ML-random computing <i>B</i> also computes <i>A</i>. We show that every <i>K</i>-trivial set is computable from a c.e. set of the same ML-degree. We investigate the interplay between ML-reducibility and cost functions, which are used to both measure the number of changes in a computable approximation, and the type of null sets intended to capture ML-random sequences. We show that for every cost function there is a c.e. set that is ML-complete among the sets obeying it. We characterise the <i>K</i>-trivial sets computable from a fragment of the left-c.e. random real Ω given by a computable set of bit positions. This leads to a new characterisation of strong jump-traceability.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138542268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Ramsey theory over partitions I: Positive Ramsey relations from forcing axioms 分区上的拉姆齐理论I:强迫公理的正拉姆齐关系
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2023-11-13 DOI: 10.1007/s11856-023-2573-x
Menachem Kojman, Assaf Rinot, Juris Steprāns
{"title":"Ramsey theory over partitions I: Positive Ramsey relations from forcing axioms","authors":"Menachem Kojman, Assaf Rinot, Juris Steprāns","doi":"10.1007/s11856-023-2573-x","DOIUrl":"https://doi.org/10.1007/s11856-023-2573-x","url":null,"abstract":"<p>In this series of papers we advance Ramsey theory over partitions. In this part, a correspondence between anti-Ramsey properties of partitions and chain conditions of the natural forcing notions that homogenize colorings over them is uncovered. At the level of the first uncountable cardinal this gives rise to a duality theorem under Martin’s Axiom: a function <i>p</i>: [<i>ω</i><sub>1</sub>]<sup>2</sup> → <i>ω</i> witnesses a weak negative Ramsey relation when <i>p</i> plays the role of a coloring if and only if a positive Ramsey relation holds over <i>p</i> when <i>p</i> plays the role of a partition.</p><p>The consistency of positive Ramsey relations over partitions does not stop at the first uncountable cardinal: it is established that at arbitrarily high uncountable cardinals these relations follow from forcing axioms without large cardinal strength. This result solves in particular two problems from [CKS21].</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138527018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Galois action on the lower central series of the fundamental group of the Fermat curve 费马曲线基群中下级数的伽罗瓦作用
2区 数学
Israel Journal of Mathematics Pub Date : 2023-11-13 DOI: 10.1007/s11856-023-2571-z
Rachel Davis, Rachel Pries, Kirsten Wickelgren
{"title":"The Galois action on the lower central series of the fundamental group of the Fermat curve","authors":"Rachel Davis, Rachel Pries, Kirsten Wickelgren","doi":"10.1007/s11856-023-2571-z","DOIUrl":"https://doi.org/10.1007/s11856-023-2571-z","url":null,"abstract":"","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134993185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Topological speedups for minimal Cantor systems 最小康托系统的拓扑加速
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2023-11-13 DOI: 10.1007/s11856-023-2568-7
Drew D. Ash, Nicholas S. Ormes
{"title":"Topological speedups for minimal Cantor systems","authors":"Drew D. Ash, Nicholas S. Ormes","doi":"10.1007/s11856-023-2568-7","DOIUrl":"https://doi.org/10.1007/s11856-023-2568-7","url":null,"abstract":"<p>In this paper we study speedups of dynamical systems in the topological category. Specifically, we characterize when one minimal homeomorphism on a Cantor space is the speedup of another. We go on to provide a characterization for strong speedups, i.e., when the jump function has at most one point of discontinuity. These results provide topological versions of the measure-theoretic results of Arnoux, Ornstein and Weiss, and are closely related to Giordano, Putnam and Skau’s characterization of orbit equivalence for minimal Cantor systems.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138527091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Ramsey theory over partitions II: Negative Ramsey relations and pump-up theorems 分区上的拉姆齐理论II:负拉姆齐关系和泵送定理
IF 1 2区 数学
Israel Journal of Mathematics Pub Date : 2023-11-13 DOI: 10.1007/s11856-023-2574-9
Menachem Kojman, Assaf Rinot, Juris Steprāns
{"title":"Ramsey theory over partitions II: Negative Ramsey relations and pump-up theorems","authors":"Menachem Kojman, Assaf Rinot, Juris Steprāns","doi":"10.1007/s11856-023-2574-9","DOIUrl":"https://doi.org/10.1007/s11856-023-2574-9","url":null,"abstract":"<p>In this series of papers we advance Ramsey theory over partitions. In this part, we concentrate on anti-Ramsey relations, or, as they are better known, strong colorings, and in particular solve two problems from [CKS21].</p><p>It is shown that for every infinite cardinal λ, a strong coloring on λ<sup>+</sup> by λ colors over a partition can be stretched to one with λ<sup>+</sup> colors over the same partition. Also, a sufficient condition is given for when a strong coloring witnessing Pr<sub>1</sub>(…) over a partition may be improved to witness Pr<sub>0</sub>(…).</p><p>Since the classical theory corresponds to the special case of a partition with just one cell, the two results generalize pump-up theorems due to Eisworth and Shelah, respectively.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138527017","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
ℤ/pr-hyperbolicity via homology 通过同调的n /p双曲性
2区 数学
Israel Journal of Mathematics Pub Date : 2023-11-13 DOI: 10.1007/s11856-023-2563-z
Guy Boyde
{"title":"ℤ/pr-hyperbolicity via homology","authors":"Guy Boyde","doi":"10.1007/s11856-023-2563-z","DOIUrl":"https://doi.org/10.1007/s11856-023-2563-z","url":null,"abstract":"Abstract We show that the homotopy groups of a Moore space P n ( p r ), where p r ≠ 2, are ℤ/ p s -hyperbolic for s ≤ r . Combined with work of Huang–Wu, Neisendorfer, and Theriault, this completely resolves the question of when such a Moore space is ℤ/ p s -hyperbolic for p ≥ 5, or when p = 2 and r ≥ 6. We also give a criterion in ordinary homology for a space to be ℤ/ p r -hyperbolic, and deduce some examples.","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136351461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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