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Transfer ideals and torsion in the Morava E-theory of abelian groups abelian群的Morava e理论中的迁移理想和扭转
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2020-05-23 DOI: 10.1007/s40062-020-00259-z
Tobias Barthel, Nathaniel Stapleton
{"title":"Transfer ideals and torsion in the Morava E-theory of abelian groups","authors":"Tobias Barthel,&nbsp;Nathaniel Stapleton","doi":"10.1007/s40062-020-00259-z","DOIUrl":"https://doi.org/10.1007/s40062-020-00259-z","url":null,"abstract":"<p>Let <i>A</i> be a finite abelian <i>p</i>-group of rank at least 2. We show that <span>(E^0(BA)/I_{tr})</span>, the quotient of the Morava <i>E</i>-cohomology of <i>A</i> by the ideal generated by the image of the transfers along all proper subgroups, contains <i>p</i>-torsion. The proof makes use of transchromatic character theory.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"15 2","pages":"369 - 375"},"PeriodicalIF":0.5,"publicationDate":"2020-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-020-00259-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4902717","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: 2
The universal fibration with fibre X in rational homotopy theory 有理同伦理论中纤维X的普遍纤维化
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2020-04-02 DOI: 10.1007/s40062-020-00258-0
Gregory Lupton, Samuel Bruce Smith
{"title":"The universal fibration with fibre X in rational homotopy theory","authors":"Gregory Lupton,&nbsp;Samuel Bruce Smith","doi":"10.1007/s40062-020-00258-0","DOIUrl":"https://doi.org/10.1007/s40062-020-00258-0","url":null,"abstract":"<p>Let <i>X</i> be a simply connected space with finite-dimensional rational homotopy groups. Let <span>(p_infty :UE rightarrow Bmathrm {aut}_1(X))</span> be the universal fibration of simply connected spaces with fibre <i>X</i>. We give a DG Lie algebra model for the evaluation map <span>( omega :mathrm {aut}_1(Bmathrm {aut}_1(X_mathbb {Q})) rightarrow Bmathrm {aut}_1(X_mathbb {Q}))</span> expressed in terms of derivations of the relative Sullivan model of <span>(p_infty )</span>. We deduce formulas for the rational Gottlieb group and for the evaluation subgroups of the classifying space <span>(Bmathrm {aut}_1(X_mathbb {Q}))</span> as a consequence. We also prove that <span>(mathbb {C} P^n_mathbb {Q})</span> cannot be realized as <span>(Bmathrm {aut}_1(X_mathbb {Q}))</span> for <span>(n le 4)</span> and <i>X</i> with finite-dimensional rational homotopy groups.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"15 2","pages":"351 - 368"},"PeriodicalIF":0.5,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-020-00258-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4064855","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: 2
The unit of the total décalage adjunction 总量程的单位
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2020-03-19 DOI: 10.1007/s40062-020-00257-1
Viktoriya Ozornova, Martina Rovelli
{"title":"The unit of the total décalage adjunction","authors":"Viktoriya Ozornova,&nbsp;Martina Rovelli","doi":"10.1007/s40062-020-00257-1","DOIUrl":"https://doi.org/10.1007/s40062-020-00257-1","url":null,"abstract":"<p>We consider the décalage construction <span>({{,mathrm{Dec},}})</span> and its right adjoint <span>(T)</span>. These functors are induced on the category of simplicial objects valued in any bicomplete category <span>({mathcal {C}})</span> by the ordinal sum. We identify <span>(T{{,mathrm{Dec},}}X)</span> with the path object <span>(X^{Delta [1]})</span> for any simplicial object <i>X</i>. We then use this formula to produce an explicit retracting homotopy for the unit <span>(Xrightarrow T{{,mathrm{Dec},}}X)</span> of the adjunction <span>(({{,mathrm{Dec},}},T))</span>. When <span>({mathcal {C}})</span> is a category of objects of an algebraic nature, we then show that the unit is a weak equivalence of simplicial objects in <span>({mathcal {C}})</span>.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"15 2","pages":"333 - 349"},"PeriodicalIF":0.5,"publicationDate":"2020-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-020-00257-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4758741","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
An application of the h-principle to manifold calculus h原理在流形微积分中的应用
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2020-03-11 DOI: 10.1007/s40062-020-00255-3
Apurva Nakade
{"title":"An application of the h-principle to manifold calculus","authors":"Apurva Nakade","doi":"10.1007/s40062-020-00255-3","DOIUrl":"https://doi.org/10.1007/s40062-020-00255-3","url":null,"abstract":"<p>Manifold calculus is a form of functor calculus that analyzes contravariant functors from some categories of manifolds to topological spaces by providing <i>analytic approximations</i> to them. In this paper, using the technique of the <i>h</i>-principle, we show that for a symplectic manifold <i>N</i>, the analytic approximation to the Lagrangian embeddings functor <span>(mathrm {Emb}_{mathrm {Lag}}(-,N))</span> is the totally real embeddings functor <span>(mathrm {Emb}_{mathrm {TR}}(-,N))</span>. More generally, for subsets <span>({mathcal {A}})</span> of the <i>m</i>-plane Grassmannian bundle <span>({{,mathrm{{Gr}},}}(m,TN))</span> for which the <i>h</i>-principle holds for <span>({mathcal {A}})</span>-directed embeddings, we prove the analyticity of the <span>({mathcal {A}})</span>-directed embeddings functor <span>({{,mathrm{Emb},}}_{{mathcal {A}}}(-,N))</span>.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"15 2","pages":"309 - 322"},"PeriodicalIF":0.5,"publicationDate":"2020-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-020-00255-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4471259","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
Correction to: Representations are adjoint to endomorphisms 更正:表示是伴随自同态的
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2020-03-06 DOI: 10.1007/s40062-020-00253-5
Gabriel C. Drummond-Cole, Joseph Hirsh, Damien Lejay
{"title":"Correction to: Representations are adjoint to endomorphisms","authors":"Gabriel C. Drummond-Cole,&nbsp;Joseph Hirsh,&nbsp;Damien Lejay","doi":"10.1007/s40062-020-00253-5","DOIUrl":"https://doi.org/10.1007/s40062-020-00253-5","url":null,"abstract":"","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"15 2","pages":"395 - 395"},"PeriodicalIF":0.5,"publicationDate":"2020-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-020-00253-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4265973","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
On the capacity and depth of compact surfaces 关于密实曲面的容量和深度
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2020-02-12 DOI: 10.1007/s40062-020-00254-4
Mahboubeh Abbasi, Behrooz Mashayekhy
{"title":"On the capacity and depth of compact surfaces","authors":"Mahboubeh Abbasi,&nbsp;Behrooz Mashayekhy","doi":"10.1007/s40062-020-00254-4","DOIUrl":"https://doi.org/10.1007/s40062-020-00254-4","url":null,"abstract":"<p>K. Borsuk in 1979, at the Topological Conference in Moscow, introduced the concept of capacity and depth of a compactum. In this paper we compute the capacity and depth of compact surfaces. We show that the capacity and depth of every compact orientable surface of genus <span>(gge 0)</span> is equal to <span>(g+2)</span>. Also, we prove that the capacity and depth of a compact non-orientable surface of genus <span>(g&gt;0)</span> is <span>([frac{g}{2}]+2)</span>.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"15 2","pages":"301 - 308"},"PeriodicalIF":0.5,"publicationDate":"2020-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-020-00254-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4492964","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: 2
Representations are adjoint to endomorphisms 表征是伴随自同态的
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2019-12-30 DOI: 10.1007/s40062-019-00252-1
Gabriel C. Drummond-Cole, Joseph Hirsh, Damien Lejay
{"title":"Representations are adjoint to endomorphisms","authors":"Gabriel C. Drummond-Cole,&nbsp;Joseph Hirsh,&nbsp;Damien Lejay","doi":"10.1007/s40062-019-00252-1","DOIUrl":"https://doi.org/10.1007/s40062-019-00252-1","url":null,"abstract":"<p>The functor that takes a ring to its category of modules has an adjoint if one remembers the forgetful functor to abelian groups: the <i>endomorphism ring</i> of linear natural transformations. This uses the self-enrichment of the category of abelian groups. If one considers enrichments into symmetric sequences or even bisymmetric sequences, one can produce an <i>endomorphism operad</i> or an <i>endomorphism properad</i>. In this note, we show that more generally, given a category <img> enriched in a monoidal category <img>, the functor that associates to a monoid in <img> its category of representations in <img> is adjoint to the functor that computes the <i>endomorphism monoid</i> of any functor with domain <img>. After describing the first results of the theory we give several examples of applications.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"15 2","pages":"377 - 393"},"PeriodicalIF":0.5,"publicationDate":"2019-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-019-00252-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5143948","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: 1
Formulae in noncommutative Hodge theory 非交换霍奇理论中的公式
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2019-11-21 DOI: 10.1007/s40062-019-00251-2
Nick Sheridan
{"title":"Formulae in noncommutative Hodge theory","authors":"Nick Sheridan","doi":"10.1007/s40062-019-00251-2","DOIUrl":"https://doi.org/10.1007/s40062-019-00251-2","url":null,"abstract":"<p>We prove that the cyclic homology of a saturated <span>(A_infty )</span> category admits the structure of a ‘polarized variation of Hodge structures’, building heavily on the work of many authors: the main point of the paper is to present complete proofs, and also explicit formulae for all of the relevant structures. This forms part of a project of Ganatra, Perutz and the author, to prove that homological mirror symmetry implies enumerative mirror symmetry.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"15 1","pages":"249 - 299"},"PeriodicalIF":0.5,"publicationDate":"2019-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-019-00251-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5135889","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: 33
The depth of a Riemann surface and of a right-angled Artin group 黎曼曲面和直角阿廷群的深度
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2019-11-12 DOI: 10.1007/s40062-019-00250-3
Yves Félix, Steve Halperin
{"title":"The depth of a Riemann surface and of a right-angled Artin group","authors":"Yves Félix,&nbsp;Steve Halperin","doi":"10.1007/s40062-019-00250-3","DOIUrl":"https://doi.org/10.1007/s40062-019-00250-3","url":null,"abstract":"<p>We consider two families of spaces, <i>X</i>: the closed orientable Riemann surfaces of genus <span>(g&gt;0)</span> and the classifying spaces of right-angled Artin groups. In both cases we compare the depth of the fundamental group with the depth of an associated Lie algebra, <i>L</i>, that can be determined by the minimal Sullivan algebra. For these spaces we prove that </p><p>and give precise formulas for the depth.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"15 1","pages":"223 - 248"},"PeriodicalIF":0.5,"publicationDate":"2019-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-019-00250-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4506940","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: 2
Lie theory for symmetric Leibniz algebras 对称莱布尼兹代数的李论
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2019-10-05 DOI: 10.1007/s40062-019-00248-x
Mamuka Jibladze, Teimuraz Pirashvili
{"title":"Lie theory for symmetric Leibniz algebras","authors":"Mamuka Jibladze,&nbsp;Teimuraz Pirashvili","doi":"10.1007/s40062-019-00248-x","DOIUrl":"https://doi.org/10.1007/s40062-019-00248-x","url":null,"abstract":"<p>Lie algebras and groups equipped with a multiplication <span>(mu )</span> satisfying some compatibility properties are studied. These structures are called symmetric Lie <span>(mu )</span>-algebras and symmetric <span>(mu )</span>-groups respectively. An equivalence of categories between symmetric Lie <span>(mu )</span>-algebras and symmetric Leibniz algebras is established when 2 is invertible in the base ring. The second main result of the paper is an equivalence of categories between simply connected symmetric Lie <span>(mu )</span>-groups and finite dimensional symmetric Leibniz algebras.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"15 1","pages":"167 - 183"},"PeriodicalIF":0.5,"publicationDate":"2019-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-019-00248-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4231021","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: 1
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