Bulletin of the London Mathematical Society最新文献

{"title":"More unit distances in arbitrary norms","authors":"Josef Greilhuber, Carl Schildkraut, Jonathan Tidor","doi":"10.1112/blms.70133","DOIUrl":"10.1112/blms.70133","url":null,"abstract":"<p>For <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 <mo>⩾</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$dgeqslant 2$</annotation>\u0000 </semantics></math> and any norm on <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>d</mi>\u0000 </msup>\u0000 <annotation>$mathbb {R}^d$</annotation>\u0000 </semantics></math>, we prove that there exists a set of <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math> points that spans at least <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mstyle>\u0000 <mfrac>\u0000 <mi>d</mi>\u0000 <mn>2</mn>\u0000 </mfrac>\u0000 </mstyle>\u0000 <mo>−</mo>\u0000 <mi>o</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mi>n</mi>\u0000 <msub>\u0000 <mi>log</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation>$(tfrac{d}{2}-o(1))nlog _2n$</annotation>\u0000 </semantics></math> unit distances under this norm for every <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>. This matches the upper bound recently proved by Alon, Bucić, and Sauermann for typical norms (i.e., norms lying in a comeagre set). We also show that for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 <mo>⩾</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$dgeqslant 3$</annotation>\u0000 </semantics></math> and a typical norm on <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>d</mi>\u0000 </msup>\u0000 <annotation>$mathbb {R}^d$</annotation>\u0000 </semantics></math>, the unit distance graph of this norm contains a copy of <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>K</mi>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 <mo>,</mo>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$K_{d,m}$</annotation>\u0000 </semantics></math> for all <span></span><math>\u0000 <semantics>\u0000 <mi>m</mi>\u0000 <annot","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 9","pages":"2885-2901"},"PeriodicalIF":0.9,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145022368","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":"Erdős space in Julia sets","authors":"David S. Lipham","doi":"10.1112/blms.70131","DOIUrl":"10.1112/blms.70131","url":null,"abstract":"<p>We prove that the rational Hilbert space, known as the <i>Erdős space</i> <span></span><math>\u0000 <semantics>\u0000 <mi>E</mi>\u0000 <annotation>$mathfrak {E}$</annotation>\u0000 </semantics></math>, surfaces in complex dynamics via iteration of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>e</mi>\u0000 <mi>z</mi>\u0000 </msup>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$e^z-1$</annotation>\u0000 </semantics></math>. More precisely, <span></span><math>\u0000 <semantics>\u0000 <mi>E</mi>\u0000 <annotation>$mathfrak {E}$</annotation>\u0000 </semantics></math> is topologically equivalent to the set of endpoints of the Julia set <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>J</mi>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>e</mi>\u0000 <mi>z</mi>\u0000 </msup>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$J(e^z-1)$</annotation>\u0000 </semantics></math> whose orbits tend to infinity in the imaginary direction.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 9","pages":"2854-2864"},"PeriodicalIF":0.9,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145021912","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":"Rational normal curves in weighted projective space","authors":"Caitlin M. Davis,&nbsp;Aleksandra Sobieska","doi":"10.1112/blms.70129","DOIUrl":"10.1112/blms.70129","url":null,"abstract":"<p>This article aims to extend classical homological results about the rational normal curves to analogues in weighted projective spaces. Results include determinantality and nonstandard versions of quadratic generation and the Koszul property.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 9","pages":"2816-2837"},"PeriodicalIF":0.9,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70129","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145021750","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":"On the Artin vanishing theorem for Stein spaces","authors":"Olivier Benoist","doi":"10.1112/blms.70124","DOIUrl":"10.1112/blms.70124","url":null,"abstract":"<p>Artin vanishing theorems for Stein spaces refer to the vanishing of some of their (co)homology groups in degrees higher than the dimension. We obtain new positive and negative results concerning Artin vanishing for the cohomology of a Stein space relative to a Runge open subset. We also prove an Artin vanishing theorem for the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Gal</mi>\u0000 <mo>(</mo>\u0000 <mi>C</mi>\u0000 <mo>/</mo>\u0000 <mi>R</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathrm{Gal}(mathbb {C}/mathbb {R})$</annotation>\u0000 </semantics></math>-equivariant cohomology of a <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Gal</mi>\u0000 <mo>(</mo>\u0000 <mi>C</mi>\u0000 <mo>/</mo>\u0000 <mi>R</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathrm{Gal}(mathbb {C}/mathbb {R})$</annotation>\u0000 </semantics></math>-equivariant Stein space relative to the fixed locus.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 9","pages":"2757-2769"},"PeriodicalIF":0.9,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145021752","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":"An infinite clique of high-filling rays in the plane minus a Cantor set","authors":"Juliette Bavard","doi":"10.1112/blms.70126","DOIUrl":"10.1112/blms.70126","url":null,"abstract":"<p>The study of the mapping class group of the plane minus a Cantor set uses a graph of loops, which is an analogous of the curve graph in the study of mapping class groups of compact surfaces. The Gromov boundary of this loop graph can be described in terms of “cliques of high-filling rays”: high-filling rays are simple geodesics of the surface which are complicated enough to be infinitely far away from any loop in the graph. Moreover, these rays are arranged in cliques: any two high-filling rays which are both disjoint from a third one are necessarily mutually disjoint. Every such clique is a point of the Gromov boundary of the loop graph. Some examples of cliques with any finite number of high-filling rays are already known.</p><p>In this paper, we construct an infinite clique of high-filling rays.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 9","pages":"2789-2798"},"PeriodicalIF":0.9,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145022349","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 the universal pairing for 2-complexes","authors":"Mikhail Khovanov,&nbsp;Vyacheslav Krushkal,&nbsp;John Nicholson","doi":"10.1112/blms.70130","DOIUrl":"10.1112/blms.70130","url":null,"abstract":"<p>The universal pairing for manifolds was defined and shown to lack positivity in dimension 4 in [Freedman, Kitaev, Nayak, Slingerland, Walker, and Wang, J. Geom. Topol. <b>9</b> (2005), 2303–2317]. We prove an analogous result for 2-complexes, and show that the universal pairing does not detect the difference between simple homotopy equivalence and 3-deformations. The question of whether these two equivalence relations are different for 2-complexes is the subject of the Andrews–Curtis conjecture. We also discuss the universal pairing for higher dimensional complexes and show that it is not positive.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 9","pages":"2838-2853"},"PeriodicalIF":0.9,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70130","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145022348","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":"Erratum: Symplectic involutions of \u0000 \u0000 \u0000 K\u0000 \u0000 3\u0000 \u0000 [\u0000 n\u0000 ]\u0000 \u0000 \u0000 \u0000 $K3^{[n]}$\u0000 type and Kummer n type manifolds","authors":"Ljudmila Kamenova,&nbsp;Giovanni Mongardi,&nbsp;Alexei Oblomkov","doi":"10.1112/blms.70128","DOIUrl":"10.1112/blms.70128","url":null,"abstract":"<p>In this note, we present a corrected formula for the enumeration of connected components of the locus fixed by a symplectic involution inside hyperkähler manifolds of types <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>K</mi>\u0000 <msup>\u0000 <mn>3</mn>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 <mi>n</mi>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$K3^{[n]}$</annotation>\u0000 </semantics></math> and generalized Kummer. We also provide further precisions concerning the involutions considered in the Kummer case.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 7","pages":"2235-2237"},"PeriodicalIF":0.9,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70128","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144681562","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":"Generators of top cohomology","authors":"Manoj Kummini,&nbsp;Mohit Upmanyu","doi":"10.1112/blms.70132","DOIUrl":"10.1112/blms.70132","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;annotation&gt;$R$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a commutative Noetherian ring and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;f&lt;/mi&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;mo&gt;Spec&lt;/mo&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$f: X longrightarrow operatorname{Spec}R$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; a proper smooth morphism, of relative dimension &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;annotation&gt;$n$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. From Hartshorne, &lt;i&gt;Residues and Duality&lt;/i&gt;, Springer, 1966, one knows that the trace map &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mo&gt;Tr&lt;/mo&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mo&gt;H&lt;/mo&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msup&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;msub&gt;\u0000 &lt;mi&gt;ω&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;⟶&lt;/mo&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$operatorname{Tr}_f: operatorname{H}^n(X, omega _{X/R}) longrightarrow R$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is an isomorphism when &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; has geometrically connected fibres. We construct an exact sequence that generates &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mo&gt;Ext&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;O&lt;/mi&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ω&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mo&gt;H&lt;/mo&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 ","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 9","pages":"2865-2884"},"PeriodicalIF":0.9,"publicationDate":"2025-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145022396","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":"Cohomology of type \u0000 \u0000 B\u0000 $B$\u0000 real permutohedral varieties","authors":"Younghan Yoon","doi":"10.1112/blms.70125","DOIUrl":"10.1112/blms.70125","url":null,"abstract":"<p>Type <span></span><math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math> and type <span></span><math>\u0000 <semantics>\u0000 <mi>B</mi>\u0000 <annotation>$B$</annotation>\u0000 </semantics></math> permutohedral varieties are classic examples of mathematics, and their topological invariants are well-known. This naturally leads to the investigation of the topology of their real loci, known as type <span></span><math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math> and type <span></span><math>\u0000 <semantics>\u0000 <mi>B</mi>\u0000 <annotation>$B$</annotation>\u0000 </semantics></math> real permutohedral varieties. The rational cohomology rings of type <span></span><math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math> real permutohedral varieties are fully described in terms of alternating permutations. Until now, only rational Betti numbers of type <span></span><math>\u0000 <semantics>\u0000 <mi>B</mi>\u0000 <annotation>$B$</annotation>\u0000 </semantics></math> real permutohedral varieties have been described in terms of <span></span><math>\u0000 <semantics>\u0000 <mi>B</mi>\u0000 <annotation>$B$</annotation>\u0000 </semantics></math>-snakes. In this paper, we explicitly describe the multiplicative structure of the cohomology rings of type <span></span><math>\u0000 <semantics>\u0000 <mi>B</mi>\u0000 <annotation>$B$</annotation>\u0000 </semantics></math> real permutohedral varieties in terms of <span></span><math>\u0000 <semantics>\u0000 <mi>B</mi>\u0000 <annotation>$B$</annotation>\u0000 </semantics></math>-snakes.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 9","pages":"2770-2788"},"PeriodicalIF":0.9,"publicationDate":"2025-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145022395","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":"Faber's socle intersection numbers via Gromov–Witten theory of elliptic curve","authors":"Xavier Blot,&nbsp;Sergey Shadrin,&nbsp;Ishan Jaztar Singh","doi":"10.1112/blms.70117","DOIUrl":"10.1112/blms.70117","url":null,"abstract":"<p>The goal of this very short note is to give a new proof of Faber's formula for the socle intersection numbers in the tautological ring of <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>M</mi>\u0000 <mi>g</mi>\u0000 </msub>\u0000 <annotation>$mathcal {M}_g$</annotation>\u0000 </semantics></math>. This new proof exhibits a new beautiful tautological relation that stems from the recent work of Oberdieck–Pixton on the Gromov–Witten theory of the elliptic curve via a refinement of their argument, and some straightforward computation with the double ramification cycles that enters the recursion relations for the Hamiltonians of the KdV hierarchy.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 9","pages":"2698-2707"},"PeriodicalIF":0.9,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70117","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145021814","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}