Bulletin of the London Mathematical Society最新文献

{"title":"A note on relative Gelfand–Fuks cohomology of spheres","authors":"Nils Prigge","doi":"10.1112/blms.70357","DOIUrl":"https://doi.org/10.1112/blms.70357","url":null,"abstract":"<p>We study the Gelfand–Fuks cohomology of smooth vector fields on <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mi>d</mi>\u0000 </msup>\u0000 <annotation>$mathbb {S}^d$</annotation>\u0000 </semantics></math> relative to <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>SO</mi>\u0000 <mo>(</mo>\u0000 <mi>d</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathrm{SO}(d+1)$</annotation>\u0000 </semantics></math> following a method of Haefliger that uses tools from rational homotopy theory. In particular, we show that <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>B</mi>\u0000 <mi>SO</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>4</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>;</mo>\u0000 <mi>R</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$H^*(mathrm{B}mathrm{SO}(4);mathbb {R})$</annotation>\u0000 </semantics></math> injects into the relative Gelfand–Fuks cohomology which corrects a claim by Haefliger. Moreover, for <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mn>3</mn>\u0000 </msup>\u0000 <annotation>$mathbb {S}^3$</annotation>\u0000 </semantics></math> the relative Gelfand–Fuks cohomology agrees with the smooth cohomology of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>Diff</mi>\u0000 <mo>+</mo>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mn>3</mn>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathrm{Diff}^+(mathbb {S}^3)$</annotation>\u0000 </semantics></math> and we provide a computation in low degrees.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 5","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70357","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147715219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hausdorff dimension of double-base expansions and binary shifts with a hole","authors":"Jian Lu,&nbsp;Wolfgang Steiner,&nbsp;Yuru Zou","doi":"10.1112/blms.70344","DOIUrl":"https://doi.org/10.1112/blms.70344","url":null,"abstract":"<p>For two real bases <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>q</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>q</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>&gt;</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$q_0, q_1 &gt; 1$</annotation>\u0000 </semantics></math>, a binary sequence <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>i</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <msub>\u0000 <mi>i</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mi>⋯</mi>\u0000 <mo>∈</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mo>{</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>}</mo>\u0000 </mrow>\u0000 <mi>∞</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$i_1 i_2 cdots in lbrace 0,1rbrace ^infty$</annotation>\u0000 </semantics></math> is the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>q</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>q</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(q_0,q_1)$</annotation>\u0000 </semantics></math>-expansion of the number\u0000\u0000 </p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70344","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147715314","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Graph morphisms as groupoid actors","authors":"Gilles G. de Castro,&nbsp;Ralf Meyer","doi":"10.1112/blms.70339","DOIUrl":"https://doi.org/10.1112/blms.70339","url":null,"abstract":"<p>We describe proper actors from the underlying groupoid of a graph <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>$textup C^*$</annotation>\u0000 </semantics></math>-algebra to another étale groupoid in terms of bisections. This allows to understand graph morphisms and the *-homomorphisms that they induce more conceptually. More generally, we describe actors from the groupoid model of a groupoid correspondence to any étale groupoid. This also covers the groupoids associated to self-similar groups and self-similar graphs, among others.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147666211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Certifying Anosov representations","authors":"J. Maxwell Riestenberg","doi":"10.1112/blms.70342","DOIUrl":"https://doi.org/10.1112/blms.70342","url":null,"abstract":"<p>By providing new finite criteria which certify that a finitely generated subgroup of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>SL</mo>\u0000 <mo>(</mo>\u0000 <mi>d</mi>\u0000 <mo>,</mo>\u0000 <mrow>\u0000 <mo>R</mo>\u0000 </mrow>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$operatorname{SL}(d,operatorname{mathbb {R}})$</annotation>\u0000 </semantics></math> or <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>SL</mo>\u0000 <mo>(</mo>\u0000 <mi>d</mi>\u0000 <mo>,</mo>\u0000 <mi>C</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$operatorname{SL}(d,mathbb {C})$</annotation>\u0000 </semantics></math> is projective Anosov, we obtain a practical algorithm to verify the Anosov condition. We demonstrate on a surface group of genus 2 in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>SL</mi>\u0000 <mo>(</mo>\u0000 <mn>3</mn>\u0000 <mo>,</mo>\u0000 <mi>R</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathrm{SL}(3,mathbb {R})$</annotation>\u0000 </semantics></math> by verifying the criteria for all words of length 8. The previous version required checking all words of length 2 million.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70342","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147666292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Convex cocompact groups in real hyperbolic spaces with limit set a Pontryagin sphere","authors":"Sami Douba,&nbsp;Gye-Seon Lee,&nbsp;Ludovic Marquis,&nbsp;Lorenzo Ruffoni","doi":"10.1112/blms.70319","DOIUrl":"https://doi.org/10.1112/blms.70319","url":null,"abstract":"<p>We exhibit two examples of convex cocompact subgroups of the isometry groups of real hyperbolic spaces with limit set a Pontryagin sphere: one generated by 50 reflections of <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mn>4</mn>\u0000 </msup>\u0000 <annotation>$mathbb {H}^4$</annotation>\u0000 </semantics></math>, and the other by a rotation of order 21 and a reflection of <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mn>6</mn>\u0000 </msup>\u0000 <annotation>$mathbb {H}^6$</annotation>\u0000 </semantics></math>. For each of them, we also locate convex cocompact subgroups with limit set a Menger curve.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147666263","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hypergraphs with arbitrarily small codegree Turán density","authors":"Simón Piga,&nbsp;Bjarne Schülke","doi":"10.1112/blms.70348","DOIUrl":"https://doi.org/10.1112/blms.70348","url":null,"abstract":"&lt;p&gt;The codegree Turán density &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;γ&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$gamma (F)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of a &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;annotation&gt;$k$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-graph &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;annotation&gt;$F$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is the smallest &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;γ&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mo&gt;[&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$gamma in [0,1)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; such that every &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;annotation&gt;$k$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-graph &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;annotation&gt;$H$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;δ&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;⩾&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;γ&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;o&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mi&gt;V&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$delta _{k-1}(H)geqslant (gamma +o(1))vert V(H)vert$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; contains a copy of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 ","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70348","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147666265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Non-amenability of mapping class groups of infinite-type surfaces and graphs","authors":"Yusen Long","doi":"10.1112/blms.70345","DOIUrl":"https://doi.org/10.1112/blms.70345","url":null,"abstract":"<p>This paper completely determines the non-amenability of the mapping class groups of infinite-type surfaces, the mapping class groups of locally finite infinite graphs of higher ranks, gives an example of non-amenable stabiliser of a point at infinity of a coarsely bounded generated hyperbolic Polish group, and exhibits a class of mapping class groups of trees or rank-one graphs that are amenable.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147666262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On virtual chirality of 3-manifolds","authors":"Hongbin Sun,&nbsp;Zhongzi Wang","doi":"10.1112/blms.70341","DOIUrl":"https://doi.org/10.1112/blms.70341","url":null,"abstract":"<p>We prove that if a prime 3-manifold <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math> is not finitely covered by the 3-sphere or a product manifold, then <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math> is virtually chiral, that is, it has a finite cover that does not admit an orientation-reversing self-homeomorphism. In general, if a 3-manifold contains a virtually chiral prime summand, then it is virtually chiral.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70341","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147666264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A remark on inverse limits of effective subshifts","authors":"Sebastián Barbieri,&nbsp;Leo Poirier","doi":"10.1112/blms.70277","DOIUrl":"https://doi.org/10.1112/blms.70277","url":null,"abstract":"<p>We show that, for every finitely generated group with decidable word problem and undecidable domino problem, there exists a sequence of effective subshifts, whose inverse limit is not the topological factor of any effective dynamical system. This follows from considerations on the universality under topological factors for this class of dynamical systems.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147637175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A classification of Prüfer domains of integer-valued polynomials on algebras","authors":"Giulio Peruginelli,&nbsp;Nicholas J. Werner","doi":"10.1112/blms.70346","DOIUrl":"https://doi.org/10.1112/blms.70346","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;annotation&gt;$D$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be an integrally closed domain with quotient field &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;annotation&gt;$K$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;annotation&gt;$A$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; a torsion-free &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;annotation&gt;$D$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-algebra that is finitely generated as a &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;annotation&gt;$D$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-module and such that &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;mo&gt;∩&lt;/mo&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Acap K=D$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. We give a complete classification of those &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;annotation&gt;$D$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;annotation&gt;$A$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; for which the ring &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;I&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;{&lt;/mo&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;[&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;]&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;∣&lt;/mo&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;⊆&lt;/mo&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;mo&gt;}&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$textnormal {Int}_K(A)=lbrace fin K[X] mid f(A)subseteq Arbrace$&lt;/annotation&gt;\u0000 &lt;/semantic","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70346","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147569059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}