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Dicritical foliations and semiroots of plane branches 平面分支的二临界叶形和半根
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2024-07-18 DOI: 10.1016/j.exmath.2024.125591
{"title":"Dicritical foliations and semiroots of plane branches","authors":"","doi":"10.1016/j.exmath.2024.125591","DOIUrl":"10.1016/j.exmath.2024.125591","url":null,"abstract":"<div><p>In this work we describe dicritical foliations in <span><math><mrow><mo>(</mo><msup><mrow><mi>ℂ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mn>0</mn><mo>)</mo></mrow></math></span> at a triple point of the resolution dual graph of an analytic plane branch <span><math><mi>C</mi></math></span> using its semiroots. In particular, we obtain a constructive method to present a one-parameter family <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>u</mi></mrow></msub></math></span> of separatrices for such foliations. As a by-product we relate the contact order between a special member of <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>u</mi></mrow></msub></math></span> and <span><math><mi>C</mi></math></span> with analytic discrete invariants of plane branches.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0723086924000586/pdfft?md5=3299d7524f5c5d739013dc887d4e9582&pid=1-s2.0-S0723086924000586-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141880878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Characterising the Haar measure on the [formula omitted]-adic rotation groups via inverse limits of measure spaces 通过度量空间的逆极限表征[公式省略]自旋群的哈氏度量
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2024-07-17 DOI: 10.1016/j.exmath.2024.125592
Paolo Aniello, Sonia L’Innocente, Stefano Mancini, Vincenzo Parisi, Ilaria Svampa, Andreas Winter
{"title":"Characterising the Haar measure on the [formula omitted]-adic rotation groups via inverse limits of measure spaces","authors":"Paolo Aniello, Sonia L’Innocente, Stefano Mancini, Vincenzo Parisi, Ilaria Svampa, Andreas Winter","doi":"10.1016/j.exmath.2024.125592","DOIUrl":"https://doi.org/10.1016/j.exmath.2024.125592","url":null,"abstract":"We determine the Haar measure on the compact -adic special orthogonal groups of rotations in dimension , by exploiting the machinery of inverse limits of measure spaces, for every prime . We characterise the groups as inverse limits of finite groups, of which we provide parametrisations and orders, together with an equivalent description through a multivariable Hensel lifting. Supplying these finite groups with their normalised counting measures, we get an inverse family of Haar measure spaces for each . Finally, we constructively prove the existence of the so-called inverse limit measure of these inverse families, which is explicitly computable, and prove that it gives the Haar measure on . Our results pave the way towards the study of the irreducible projective unitary representations of the -adic rotation groups, with potential applications to the recently proposed -adic quantum information theory.","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141880872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Root involutions, real forms and diagrams 根渐开线、实数形式和图表
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2024-07-16 DOI: 10.1016/j.exmath.2024.125593
{"title":"Root involutions, real forms and diagrams","authors":"","doi":"10.1016/j.exmath.2024.125593","DOIUrl":"10.1016/j.exmath.2024.125593","url":null,"abstract":"<div><p>We study the correspondence between equivalence classes of pairs consisting of real semisimple Lie algebras and their Cartan subalgebras and involutions of the corresponding root system. This can be graphically described by introducing <span><math><mrow><mi>S</mi><mspace></mspace></mrow></math></span>- and <span><math><mi>Σ</mi></math></span>-<em>diagrams</em>, generalizing those of Satake and Vogan.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0723086924000604/pdfft?md5=445995afea316cbdb564083c3930d697&pid=1-s2.0-S0723086924000604-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141713250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Relative sectional category revisited 重新审视相对断面类别
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2024-07-11 DOI: 10.1016/j.exmath.2024.125590
{"title":"Relative sectional category revisited","authors":"","doi":"10.1016/j.exmath.2024.125590","DOIUrl":"10.1016/j.exmath.2024.125590","url":null,"abstract":"<div><p>The concept of relative sectional category expands upon classical sectional category theory by incorporating the pullback of a fibration along a map. Our paper aims not only to explore this extension but also to thoroughly investigate its properties. We seek to uncover how the relative sectional category unifies several homotopic numerical invariants found in recent literature. These include the topological complexity of maps according to Murillo–Wu or Scott, relative topological complexity as defined by Farber, and homotopic distance for continuous maps in the sense of Macías-Virgós and Mosquera-Lois, among others.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0723086924000574/pdfft?md5=e497014632089ab2358c7bdb9c539959&pid=1-s2.0-S0723086924000574-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141736433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On ordinary isogeny graphs with level structures 关于具有水平结构的普通等值图
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2024-07-05 DOI: 10.1016/j.exmath.2024.125589
{"title":"On ordinary isogeny graphs with level structures","authors":"","doi":"10.1016/j.exmath.2024.125589","DOIUrl":"10.1016/j.exmath.2024.125589","url":null,"abstract":"<div><p>Let <span><math><mi>ℓ</mi></math></span> and <span><math><mi>p</mi></math></span> be two distinct prime numbers. We study <span><math><mi>ℓ</mi></math></span>-isogeny graphs of ordinary elliptic curves defined over a finite field of characteristic <span><math><mi>p</mi></math></span>, together with a level structure. Firstly, we show that as the level varies over all <span><math><mi>p</mi></math></span>-powers, the graphs form an Iwasawa-theoretic abelian <span><math><mi>p</mi></math></span>-tower, which can be regarded as a graph-theoretical analogue of the Igusa tower of modular curves. Secondly, we study the structure of the crater of these graphs, generalizing previous results on volcano graphs. Finally, we solve an inverse problem of graphs arising from the crater of <span><math><mi>ℓ</mi></math></span>-isogeny graphs with level structures, partially generalizing a recent result of Bambury, Campagna and Pazuki.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0723086924000562/pdfft?md5=421a5d8db9c34e0de0dd8471dd9d689a&pid=1-s2.0-S0723086924000562-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141736432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On convergence of points to limiting processes, with an application to zeta zeros 论点向极限过程的收敛，并应用于 zeta 零点
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2024-07-04 DOI: 10.1016/j.exmath.2024.125588
{"title":"On convergence of points to limiting processes, with an application to zeta zeros","authors":"","doi":"10.1016/j.exmath.2024.125588","DOIUrl":"10.1016/j.exmath.2024.125588","url":null,"abstract":"<div><p>This paper considers sequences of points on the real line which have been randomly translated, and provides conditions under which various notions of convergence to a limiting point process are equivalent. In particular we consider convergence in correlation, convergence in distribution, and convergence of spacings between points. We also prove a simple Tauberian theorem regarding rescaled correlations. The results are applied to zeros of the Riemann zeta-function to show that several ways to state the GUE Hypothesis are equivalent. The proof relies on a moment bound of A. Fujii.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141880857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Products of boundary classes on M¯0,n via balanced weights 通过平衡加权的 M¯0,n 上边界类的乘积
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2024-07-01 DOI: 10.1016/j.exmath.2024.125587
Maria Gillespie , Jake Levinson
{"title":"Products of boundary classes on M¯0,n via balanced weights","authors":"Maria Gillespie ,&nbsp;Jake Levinson","doi":"10.1016/j.exmath.2024.125587","DOIUrl":"https://doi.org/10.1016/j.exmath.2024.125587","url":null,"abstract":"<div><p>In this note, we give a simple closed formula for an arbitrary product, landing in dimension 0, of boundary classes on the Deligne–Mumford moduli space <span><math><msub><mrow><mover><mrow><mi>M</mi></mrow><mo>¯</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>n</mi></mrow></msub></math></span>. For any such boundary strata <span><math><mrow><msub><mrow><mi>X</mi></mrow><mrow><msub><mrow><mi>T</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>X</mi></mrow><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>ℓ</mi></mrow></msub></mrow></msub></mrow></math></span>, we show the intersection product <span><math><mrow><mo>∫</mo><msubsup><mrow><mo>∏</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>ℓ</mi></mrow></msubsup><mrow><mo>[</mo><msub><mrow><mi>X</mi></mrow><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>]</mo></mrow></mrow></math></span> is either a signed product of multinomial coefficients, or zero, and provide a simple criterion for determining when it is nonzero.</p><p>We do not claim originality for our product formula, but to our knowledge it does not appear elsewhere in the literature.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141486747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Harmonic analysis of compact Lie supergroups 紧凑李超群的谐波分析
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2024-07-01 DOI: 10.1016/j.exmath.2024.125586
M.-K. Chuah, C.A. Cremonini, R. Fioresi
{"title":"Harmonic analysis of compact Lie supergroups","authors":"M.-K. Chuah, C.A. Cremonini, R. Fioresi","doi":"10.1016/j.exmath.2024.125586","DOIUrl":"https://doi.org/10.1016/j.exmath.2024.125586","url":null,"abstract":"We realize the irreducible representations of a compact Lie supergroup , with a contragredient simple Lie superalgebra, in the space of square integrable (in the sense of Berezin) holomorphic sections on , is the real torus in the complexification of . We give an explicit realization of unitary representations when .","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141614865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A survey on conjugacy class graphs of groups 群的共轭类图概览
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2024-06-04 DOI: 10.1016/j.exmath.2024.125585
Peter J. Cameron , Firdous Ee Jannat , Rajat Kanti Nath , Reza Sharafdini
{"title":"A survey on conjugacy class graphs of groups","authors":"Peter J. Cameron ,&nbsp;Firdous Ee Jannat ,&nbsp;Rajat Kanti Nath ,&nbsp;Reza Sharafdini","doi":"10.1016/j.exmath.2024.125585","DOIUrl":"https://doi.org/10.1016/j.exmath.2024.125585","url":null,"abstract":"<div><p>There are several graphs defined on groups. Among them we consider graphs whose vertex set consists conjugacy classes of a group <span><math><mi>G</mi></math></span> and adjacency is defined by properties of the elements of conjugacy classes. In particular, we consider commuting/nilpotent/solvable conjugacy class graph of <span><math><mi>G</mi></math></span> where two distinct conjugacy classes <span><math><msup><mrow><mi>a</mi></mrow><mrow><mi>G</mi></mrow></msup></math></span> and <span><math><msup><mrow><mi>b</mi></mrow><mrow><mi>G</mi></mrow></msup></math></span> are adjacent if there exist some elements <span><math><mrow><mi>x</mi><mo>∈</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>G</mi></mrow></msup></mrow></math></span> and <span><math><mrow><mi>y</mi><mo>∈</mo><msup><mrow><mi>b</mi></mrow><mrow><mi>G</mi></mrow></msup></mrow></math></span> such that <span><math><mrow><mo>〈</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>〉</mo></mrow></math></span> is abelian/nilpotent/solvable. After a section of introductory results and examples, we discuss all the available results on connectedness, graph realization, genus, various spectra and energies of certain induced subgraphs of these graphs. Proofs of the results are not included. However, many open problems for further investigation are stated.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0723086924000525/pdfft?md5=18b445b3245dc9583ae34dc4fb72277e&pid=1-s2.0-S0723086924000525-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141303423","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Proofs of ergodicity of piecewise Möbius interval maps using planar extensions 利用平面扩展证明片断莫比乌斯区间映射的遍历性
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2024-05-15 DOI: 10.1016/j.exmath.2024.125575
Kariane Calta , Cor Kraaikamp , Thomas A. Schmidt
{"title":"Proofs of ergodicity of piecewise Möbius interval maps using planar extensions","authors":"Kariane Calta ,&nbsp;Cor Kraaikamp ,&nbsp;Thomas A. Schmidt","doi":"10.1016/j.exmath.2024.125575","DOIUrl":"https://doi.org/10.1016/j.exmath.2024.125575","url":null,"abstract":"<div><p>We give two results for deducing dynamical properties of piecewise Möbius interval maps from their related planar extensions. First, eventual expansivity and the existence of an ergodic invariant probability measure equivalent to Lebesgue measure both follow from mild finiteness conditions on the planar extension along with a new property “bounded non-full range” used to relax traditional Markov conditions. Second, the “quilting” operation to appropriately nearby planar systems, introduced by Kraaikamp and co-authors, can be used to prove several key dynamical properties of a piecewise Möbius interval map. As a proof of concept, we apply these results to recover known results on the well-studied Nakada <span><math><mi>α</mi></math></span>-continued fractions; we obtain similar results for interval maps derived from an infinite family of non-commensurable Fuchsian groups.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141164254","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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