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Journal of Homotopy and Related Structures最新文献

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Normality of algebras over commutative rings and the Teichmüller class. III. 交换环上代数的正态性及teichmller类。3
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2017-07-25 DOI: 10.1007/s40062-017-0175-1
Johannes Huebschmann
{"title":"Normality of algebras over commutative rings and the Teichmüller class. III.","authors":"Johannes Huebschmann","doi":"10.1007/s40062-017-0175-1","DOIUrl":"https://doi.org/10.1007/s40062-017-0175-1","url":null,"abstract":"<p>We describe various non-trivial examples that illustrate the approach to the “Teichmüller cocycle map” developed elsewhere in terms of crossed 2-fold extensions and generalizations thereof.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"13 1","pages":"127 - 142"},"PeriodicalIF":0.5,"publicationDate":"2017-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-017-0175-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5342841","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: 3
An equivalence between semisimple symmetric Frobenius algebras and Calabi–Yau categories 半简单对称Frobenius代数与Calabi-Yau范畴之间的等价
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2017-05-30 DOI: 10.1007/s40062-017-0181-3
Jan Hesse
{"title":"An equivalence between semisimple symmetric Frobenius algebras and Calabi–Yau categories","authors":"Jan Hesse","doi":"10.1007/s40062-017-0181-3","DOIUrl":"https://doi.org/10.1007/s40062-017-0181-3","url":null,"abstract":"<p>We show that the bigroupoid of semisimple symmetric Frobenius algebras over an algebraically closed field and the bigroupoid of Calabi–Yau categories are equivalent. To this end, we construct a trace on the category of finitely-generated representations of a symmetric, semisimple Frobenius algebra, given by the composite of the Frobenius form with the Hattori-Stallings trace.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"13 1","pages":"251 - 272"},"PeriodicalIF":0.5,"publicationDate":"2017-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-017-0181-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4029148","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: 6
Massey products in differential cohomology via stacks 通过叠的微分上同调中的Massey积
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2017-05-27 DOI: 10.1007/s40062-017-0178-y
Daniel Grady, Hisham Sati
{"title":"Massey products in differential cohomology via stacks","authors":"Daniel Grady,&nbsp;Hisham Sati","doi":"10.1007/s40062-017-0178-y","DOIUrl":"https://doi.org/10.1007/s40062-017-0178-y","url":null,"abstract":"<p>We extend Massey products from cohomology to differential cohomology via stacks, organizing and generalizing existing constructions in Deligne cohomology. We study the properties and show how they are related to more classical Massey products in de Rham, singular, and Deligne cohomology. The setting and the algebraic machinery via stacks allow for computations and make the construction well-suited for applications. We illustrate with several examples from differential geometry and mathematical physics.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"13 1","pages":"169 - 223"},"PeriodicalIF":0.5,"publicationDate":"2017-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-017-0178-y","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5057961","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: 14
Symmetric multiplicative formality of the Kontsevich operad 孔采维奇算子的对称乘法形式
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2017-05-22 DOI: 10.1007/s40062-017-0179-x
Paul Arnaud Songhafouo Tsopméné
{"title":"Symmetric multiplicative formality of the Kontsevich operad","authors":"Paul Arnaud Songhafouo Tsopméné","doi":"10.1007/s40062-017-0179-x","DOIUrl":"https://doi.org/10.1007/s40062-017-0179-x","url":null,"abstract":"<p>In his famous paper entitled “Operads and motives in deformation quantization”, Maxim Kontsevich constructed (in order to prove the formality of the little <i>d</i>-disks operad) a topological operad, which is called in the literature the <i>Kontsevich operad</i>, and which is denoted <span>({mathcal {K}}_d)</span> in this paper. This operad has a nice structure: it is a <i>multiplicative symmetric operad</i>, that is, it comes with a morphism from the symmetric associative operad. There are many results in the literature regarding the formality of <span>({mathcal {K}}_d)</span>. It is well known (by Kontsevich) that <span>({mathcal {K}}_d)</span> is formal over reals as a symmetric operad. It is also well known (independently by Syunji Moriya and the author) that <span>({mathcal {K}}_d)</span> is formal as a multiplicative nonsymmetric operad. In this paper, we prove that the Kontsevich operad is formal over reals as a multiplicative symmetric operad, when <span>(d ge 3)</span>.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"13 1","pages":"225 - 235"},"PeriodicalIF":0.5,"publicationDate":"2017-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-017-0179-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4870424","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
Geometric models of twisted differential K-theory I 扭曲微分k理论的几何模型I
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2017-05-13 DOI: 10.1007/s40062-017-0177-z
Byungdo Park
{"title":"Geometric models of twisted differential K-theory I","authors":"Byungdo Park","doi":"10.1007/s40062-017-0177-z","DOIUrl":"https://doi.org/10.1007/s40062-017-0177-z","url":null,"abstract":"<p>This is the first in a series of papers constructing geometric models of twisted differential <i>K</i>-theory. In this paper we construct a model of even twisted differential <i>K</i>-theory when the underlying topological twist represents a torsion class. By differential twists we will mean smooth <i>U</i>(1)-gerbes with connection, and we use twisted vector bundles with connection as cocycles. The model we construct satisfies the axioms of Kahle and Valentino, including functoriality, naturality of twists, and the hexagon diagram. This paper confirms a long-standing hypothetical idea that twisted vector bundles with connection define twisted differential <i>K</i>-theory.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"13 1","pages":"143 - 167"},"PeriodicalIF":0.5,"publicationDate":"2017-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-017-0177-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4547231","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: 12
Principal ideals in mod-(ell ) Milnor K-theory 模型中的主要理想- (ell )米尔诺k理论
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2017-05-12 DOI: 10.1007/s40062-017-0176-0
Charles Weibel, Inna Zakharevich
{"title":"Principal ideals in mod-(ell ) Milnor K-theory","authors":"Charles Weibel,&nbsp;Inna Zakharevich","doi":"10.1007/s40062-017-0176-0","DOIUrl":"https://doi.org/10.1007/s40062-017-0176-0","url":null,"abstract":"<p>Fix a symbol <span>(underline{a})</span> in the mod-<span>(ell )</span> Milnor <i>K</i>-theory of a field <i>k</i>, and a norm variety <i>X</i> for <span>(underline{a})</span>. We show that the ideal generated by <span>(underline{a})</span> is the kernel of the <i>K</i>-theory map induced by <span>(ksubset k(X))</span> and give generators for the annihilator of the ideal. When <span>(ell =2)</span>, this was done by Orlov, Vishik and Voevodsky.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"12 4","pages":"1033 - 1049"},"PeriodicalIF":0.5,"publicationDate":"2017-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-017-0176-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4805091","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
Rational orthogonal calculus 有理正交演算
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2017-04-13 DOI: 10.1007/s40062-017-0172-4
David Barnes
{"title":"Rational orthogonal calculus","authors":"David Barnes","doi":"10.1007/s40062-017-0172-4","DOIUrl":"https://doi.org/10.1007/s40062-017-0172-4","url":null,"abstract":"<p>We show that one can use model categories to construct rational orthogonal calculus. That is, given a continuous functor from vector spaces to based spaces one can construct a tower of approximations to this functor depending only on the rational homology type of the input functor, whose layers are given by rational spectra with an action of <i>O</i>(<i>n</i>). By work of Greenlees and Shipley, we see that these layers are classified by torsion <span>({{mathrm{H}}}^*({{mathrm{B}}}SO(n))[O(n)/SO(n)])</span>-modules.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"12 4","pages":"1009 - 1032"},"PeriodicalIF":0.5,"publicationDate":"2017-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-017-0172-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4516691","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
Generalized homology and cohomolgy theories with coefficients 带系数的广义同调和上同调理论
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2017-04-06 DOI: 10.1007/s40062-017-0171-5
Inès Saihi
{"title":"Generalized homology and cohomolgy theories with coefficients","authors":"Inès Saihi","doi":"10.1007/s40062-017-0171-5","DOIUrl":"https://doi.org/10.1007/s40062-017-0171-5","url":null,"abstract":"<p>For any Moore spectrum <i>M</i> and any homology theory <span>({{mathcal {H}}}_*)</span>, we associate a homology theory <span>({{mathcal {H}}}_*^M)</span> which is related to <span>({{mathcal {H}}}_*)</span> by a universal coefficient exact sequence of classical type. On the other hand the category of Moore spectra is not the category of <span>({mathbb {Z}})</span>-modules, but it can be identified to a full subcategory of an abelian category <span>({{mathscr {D}}})</span>. We prove that <span>({{mathcal {H}}}_*)</span> can be lifted to a homology theory <span>(widehat{{mathcal {H}}}_*)</span> with values in <span>({{mathscr {D}}})</span> and we give a new universal coefficient exact sequence relating <span>({{mathcal {H}}}_*^M)</span> and <span>(widehat{{mathcal {H}}}_*)</span> which is in general more precise than the classical one. We prove also a similar result for cohomology theories and we illustrate its convenience by computing the real K-theory of Moore spaces.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"12 4","pages":"993 - 1007"},"PeriodicalIF":0.5,"publicationDate":"2017-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-017-0171-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4235523","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
The diagonal of a multicosimplicial object 多重复形物体的对角线
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2017-03-20 DOI: 10.1007/s40062-017-0169-z
Philip S. Hirschhorn
{"title":"The diagonal of a multicosimplicial object","authors":"Philip S. Hirschhorn","doi":"10.1007/s40062-017-0169-z","DOIUrl":"https://doi.org/10.1007/s40062-017-0169-z","url":null,"abstract":"<p>We show that the functor that takes a multicosimplicial object in a model category to its diagonal cosimplicial object is a right Quillen functor. This implies that the diagonal of a Reedy fibrant multicosimplicial object is a Reedy fibrant cosimplicial object, which has applications to the calculus of functors. We also show that, although the diagonal functor is a Quillen functor, it is not a Quillen equivalence for multicosimplicial spaces. We also discuss total objects and homotopy limits of multicosimplicial objects. We show that the total object of a multicosimplicial object is isomorphic to the total object of the diagonal, and that the diagonal embedding of the cosimplicial indexing category into the multicosimplicial indexing category is homotopy left cofinal, which implies that the homotopy limits are weakly equivalent if the multicosimplicial object is at least objectwise fibrant.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"12 4","pages":"971 - 992"},"PeriodicalIF":0.5,"publicationDate":"2017-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-017-0169-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4796921","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
(G )-theory of (mathbb F_1)-algebras I: the equivariant Nishida problem (G )-理论 (mathbb F_1)代数I:等变西田问题
IF 0.5 4区 数学
Journal of Homotopy and Related Structures Pub Date : 2017-02-03 DOI: 10.1007/s40062-017-0168-0
Snigdhayan Mahanta
{"title":"(G )-theory of (mathbb F_1)-algebras I: the equivariant Nishida problem","authors":"Snigdhayan Mahanta","doi":"10.1007/s40062-017-0168-0","DOIUrl":"https://doi.org/10.1007/s40062-017-0168-0","url":null,"abstract":"<p>We develop a version of <span>(G )</span>-theory for an <span>(mathbb F_1)</span>-algebra (i.e., the <span>(K )</span>-theory of pointed <i>G</i>-sets for a pointed monoid <i>G</i>) and establish its first properties. We construct a Cartan assembly map to compare the Chu–Morava <span>(K )</span>-theory for finite pointed groups with our <span>(G )</span>-theory. We compute the <span>(G )</span>-theory groups for finite pointed groups in terms of stable homotopy of some classifying spaces. We introduce certain Loday–Whitehead groups over <span>(mathbb F_1)</span> that admit functorial maps into classical Whitehead groups under some reasonable hypotheses. We initiate a conjectural formalism using combinatorial Grayson operations to address the Equivariant Nishida Problem—it asks whether <span>(mathbb {S}^G)</span> admits operations that endow <span>(oplus _npi _{2n}(mathbb {S}^G))</span> with a pre-<span>(lambda )</span>-ring structure, where <i>G</i> is a finite group and <span>(mathbb {S}^G)</span> is the <i>G</i>-fixed point spectrum of the equivariant sphere spectrum.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"12 4","pages":"901 - 930"},"PeriodicalIF":0.5,"publicationDate":"2017-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-017-0168-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4117335","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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