Israel Journal of Mathematics最新文献

{"title":"Orbit configuration spaces and the homotopy groups of the pair $$(prodnolimits_1^n {M,{F_n}} (M))$$ for M either $${mathbb{S}^2}$$ or ℝP2","authors":"Daciberg Lima Gonçalves, John Guaschi","doi":"10.1007/s11856-023-2576-7","DOIUrl":"https://doi.org/10.1007/s11856-023-2576-7","url":null,"abstract":"<p>Let <i>n</i> ≥ 1, and let <span>({iota _n}:{F_n}(M) to prodnolimits_1^n M )</span> be the natural inclusion of the <i>n</i>^th configuration space of <i>M</i> in the <i>n</i>-fold Cartesian product of <i>M</i> with itself. In this paper, we study the map <i>ι</i>_<i>n</i>, the homotopy fibre <i>I</i>_<i>n</i> of <i>ι</i>_<i>n</i> and its homotopy groups, and the induced homomorphisms (<i>ι</i>_<i>n</i>)_<i>#k</i> on the <i>k</i>^th homotopy groups of <i>F</i>_<i>n</i>(<i>M</i>) and <span>(prodnolimits_1^n M )</span> for all <i>k</i> ≥ 1, where <i>M</i> is the 2-sphere <span>({mathbb{S}^2})</span> or the real projective plane ℝ<i>P</i>².It is well known that the group π_<i>k</i>(<i>I</i>_<i>n</i>) is the homotopy group <span>({pi _{k + 1}}(prodnolimits_1^n {M,{F_n}} (M)))</span> for all <i>k</i> ≥ 0. If <i>k</i> ≥ 2, we show that the homomorphism (<i>ι</i>_<i>n</i>⁾_<i>#k</i> is injective and diagonal, with the exception of the case <i>n</i> = <i>k</i> = 2 and <span>(M = {mathbb{S}^2})</span>, where it is anti-diagonal. We then show that <i>I</i>_<i>n</i> has the homotopy type of <span>(K({R_{n - 1}},1) times Omega (prodnolimits_1^{n - 1} {{mathbb{S}^2}} ))</span>, where <i>R</i>_<i>n</i>−1 is the (<i>n</i> − 1)^th Artin pure braid group if <span>(M = {mathbb{S}^2})</span>, and is the fundamental group <i>G</i>_<i>n</i>−1 of the (<i>n</i>−1)^th orbit configuration space of the open cylinder <span>({mathbb{S}^2}backslash { {widetilde z_0}, - {widetilde z_0}} )</span> with respect to the action of the antipodal map of <span>({mathbb{S}^2})</span> if <i>M</i> = ℝ<i>P</i>², where <span>({widetilde z_0} in {mathbb{S}^2})</span>. This enables us to describe the long exact sequence in homotopy of the homotopy fibration <span>({I_n} to {F_n}(M)buildrel {{iota _n}} overlongrightarrow prodnolimits_1^n M )</span> in geometric terms, and notably the image of the boundary homomorphism <span>({pi _{k + 1}}(prodnolimits_1^n M ) to {pi _k}({I_n}))</span>. From this, if <span>(M = {mathbb{S}^2})</span> and <i>n</i> ≥ 3 (resp. <i>M</i> = ℝ<i>P</i>² and <i>n</i> ≥ 2), we show that Ker((<i>ι</i>_<i>n</i>)_#1 ) is isomorphic to the quotient of <i>R</i>_<i>n</i>−1 by the square of its centre, as well as to an iterated semi-direct product of free groups with the subgroup of order 2 generated by the centre of <i>P</i>_<i>n</i> (<i>M</i>) that is reminiscent of the combing operation for the Artin pure braid groups, as well as decompositions obtained in [GG5].</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138579441","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}

{"title":"On the Rankin–Selberg L-factors for SO5 × GL2","authors":"Yao Cheng","doi":"10.1007/s11856-023-2580-y","DOIUrl":"https://doi.org/10.1007/s11856-023-2580-y","url":null,"abstract":"<p>Let <i>π</i> and <i>τ</i> be irreducible smooth generic representations of SO₅ and GL₂ respectively over a non-archimedean local field. We show that the <i>L</i>- and <i>ε</i>-factors attached to <i>π</i>×<i>π</i> defined by the Rankin–Selberg integrals and the associated Weil–Deligne representation coincide. The proof is obtained by explicating the relation between the Rankin–Selberg integrals for SO₅ × GL₂ and Novodvorsky’s local integrals for GSp₄× GL₂.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138579629","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}

{"title":"Polynomial growth of the codimensions sequence of algebras with group graded involution","authors":"Maralice Assis de Oliveira, Rafael Bezerra dos Santos, Ana Cristina Vieira","doi":"10.1007/s11856-023-2585-6","DOIUrl":"https://doi.org/10.1007/s11856-023-2585-6","url":null,"abstract":"<p>An algebra graded by a group <i>G</i> and endowed with a graded involution * is called a (<i>G</i>, *)-algebra. Here we consider <i>G</i> a finite abelian group and classify the subvarieties of the varieties of almost polynomial growth generated by finite-dimensional (<i>G</i>, *)-algebras. Also, we present, up to equivalence, the complete list of (<i>G</i>, *)-algebras generating varieties of at most linear growth. Along the way, we give a new characterization of varieties of polynomial growth generated by finite-dimensional (<i>G</i>, *)-algebras by considering the structure of the generating algebra.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138579906","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}

{"title":"The profinite completion of relatively hyperbolic virtually special groups","authors":"Pavel Zalesskii","doi":"10.1007/s11856-023-2584-7","DOIUrl":"https://doi.org/10.1007/s11856-023-2584-7","url":null,"abstract":"<p>We give a characterization of toral relatively hyperbolic virtually special groups in terms of the profinite completion. We also prove a Tits alternative for subgroups of the profinite completion <i>Ĝ</i> of a relatively hyperbolic virtually compact special group <i>G</i> and completely describe finitely generated pro-<i>p</i> subgroups of <i>Ĝ</i>. This applies to the profinite completion of the fundamental group of a hyperbolic arithmetic manifold. We deduce that all finitely generated pro-<i>p</i> subgroups of the congruence kernel of a standard arithmetic lattice of <i>SO</i>(<i>n</i>, 1) are free pro-<i>p</i>.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138579432","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}

{"title":"Lifting (co)stratifications between tensor triangulated categories","authors":"Liran Shaul, Jordan Williamson","doi":"10.1007/s11856-023-2578-5","DOIUrl":"https://doi.org/10.1007/s11856-023-2578-5","url":null,"abstract":"<p>We give necessary and sufficient conditions for stratification and costratification to descend along a coproduct preserving, tensor-exact <i>R</i>-linear functor between <i>R</i>-linear tensor-triangulated categories which are rigidly-compactly generated by their tensor units. We then apply these results to non-positive commutative DG-rings and connective ring spectra. In particular, this gives a support-theoretic classification of (co)localizing subcategories, and thick subcategories of compact objects of the derived category of a non-positive commutative DG-ring with finite amplitude, and provides a formal justification for the principle that the space associated to an eventually coconnective derived scheme is its underlying classical scheme. For a non-positive commutative DG-ring <i>A</i>, we also investigate whether certain finiteness conditions in D(<i>A</i>) (for example, proxy-smallness) can be reduced to questions in the better understood category D(<i>H</i>⁰<i>A</i>).</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138579622","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}

{"title":"On the mean radius of quasiconformal mappings","authors":"Alastair N. Fletcher, Jacob Pratscher","doi":"10.1007/s11856-023-2583-8","DOIUrl":"https://doi.org/10.1007/s11856-023-2583-8","url":null,"abstract":"<p>We study the mean radius growth function for quasiconformal mappings. We give a new sub-class of quasiconformal mappings in ℝ^<i>n</i>, for <i>n</i> ≥ 2, called bounded integrable parameterization mappings, or BIP maps for short. These have the property that the restriction of the Zorich transform to each slice has uniformly bounded derivative in <i>L</i>^{<i>n</i>/(<i>n</i>−1)}. For BIP maps, the logarithmic transform of the mean radius function is bi-Lipschitz. We then apply our result to BIP maps with simple infinitesimal spaces to show that the asymptotic representation is indeed quasiconformal by showing that its Zorich transform is a bi-Lipschitz map.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138579427","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}

{"title":"Immersion of complete digraphs in Eulerian digraphs","authors":"António Girão, Shoham Letzter","doi":"10.1007/s11856-023-2572-y","DOIUrl":"https://doi.org/10.1007/s11856-023-2572-y","url":null,"abstract":"Abstract A digraph G immerses a digraph H if there is an injection f : V ( H ) → V ( G ) and a collection of pairwise edge-disjoint directed paths P uv , for uv ∈ E ( H ), such that P uv starts at f ( u ) and ends at f ( v ). We prove that every Eulerian digraph with minimum out-degree t immerses a complete digraph on Ω( t ) vertices, thus answering a question of DeVos, McDonald, Mohar and Scheide.","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":"134993021","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}

{"title":"Conservation strength of the infinite pigeonhole principle for trees","authors":"Chitat Chong, Wei Wang, Yue Yang","doi":"10.1007/s11856-023-2567-8","DOIUrl":"https://doi.org/10.1007/s11856-023-2567-8","url":null,"abstract":"Let TT1 be the combinatorial principle stating that every finite coloring of the infinite full binary tree has a homogeneous isomorphic subtree. Let RT 2 2 and WKL0 denote respectively the principles of Ramsey’s theorem for pairs and the weak König lemma. It is proved that TT1 + RT 2 2 + WKL0 is Π 3 0 -conservative over the base system RCA0. Thus over RCA0, TT1 and Ramsey’s theorem for pairs prove the same Π 3 0 -sentences.","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":"134993024","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}

{"title":"Wonderful compactifications of Bruhat–Tits buildings in the non-split case","authors":"Dorian Chanfi","doi":"10.1007/s11856-023-2562-0","DOIUrl":"https://doi.org/10.1007/s11856-023-2562-0","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":"134993192","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}

{"title":"An infinite interval version of the α-Kakutani equidistribution problem","authors":"Mark Pollicott, Benedict Sewell","doi":"10.1007/s11856-023-2569-6","DOIUrl":"https://doi.org/10.1007/s11856-023-2569-6","url":null,"abstract":"<p>In this article we extend results of Kakutani, Adler–Flatto, Smilansky and others on the classical <i>α</i>-Kakutani equidistribution result for sequences arising from finite partitions of the interval. In particular, we describe a generalization of the equidistribution result to infinite partitions. In addition, we give discrepancy estimates, extending results of Drmota–Infusino [8].</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":"138542262","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}