Journal of Homotopy and Related Structures最新文献_第6页

On the Maurer-Cartan simplicial set of a complete curved (A_infty )-algebra 关于完全弯曲(A_infty ) -代数的Maurer-Cartan简单集

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2021-09-25 DOI: 10.1007/s40062-021-00290-8

Niek de Kleijn, Felix Wierstra

{"title":"On the Maurer-Cartan simplicial set of a complete curved (A_infty )-algebra","authors":"Niek de Kleijn, Felix Wierstra","doi":"10.1007/s40062-021-00290-8","DOIUrl":"10.1007/s40062-021-00290-8","url":null,"abstract":"<div>In this paper, we develop the (A_infty )-analog of the Maurer-Cartan simplicial set associated to an (L_infty )-algebra and show how we can use this to study the deformation theory of (infty )-morphisms of algebras over non-symmetric operads. More precisely, we first recall and prove some of the main properties of (A_infty )-algebras like the Maurer-Cartan equation and twist. One of our main innovations here is the emphasis on the importance of the shuffle product. Then, we define a functor from the category of complete (curved) (A_infty )-algebras to simplicial sets, which sends a complete curved (A_infty )-algebra to the associated simplicial set of Maurer-Cartan elements. This functor has the property that it gives a Kan complex. In all of this, we do not require any assumptions on the field we are working over. We also show that this functor can be used to study deformation problems over a field of characteristic greater than or equal to 0. As a specific example of such a deformation problem, we study the deformation theory of (infty )-morphisms of algebras over non-symmetric operads.</div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40062-021-00290-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4986646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Quasi-categories vs. Segal spaces: Cartesian edition 准范畴与西格尔空间:笛卡尔版

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2021-08-20 DOI: 10.1007/s40062-021-00288-2

Nima Rasekh

{"title":"Quasi-categories vs. Segal spaces: Cartesian edition","authors":"Nima Rasekh","doi":"10.1007/s40062-021-00288-2","DOIUrl":"10.1007/s40062-021-00288-2","url":null,"abstract":"<div>We prove that four different ways of defining Cartesian fibrations and the Cartesian model structure are all Quillen equivalent: <ol>\u0000 <li>\u0000 1.\u0000 \u0000 On marked simplicial sets (due to Lurie [31]),\u0000 \u0000 </li>\u0000 <li>\u0000 2.\u0000 \u0000 On bisimplicial spaces (due to deBrito [12]),\u0000 \u0000 </li>\u0000 <li>\u0000 3.\u0000 \u0000 On bisimplicial sets,\u0000 \u0000 </li>\u0000 <li>\u0000 4.\u0000 \u0000 On marked simplicial spaces.\u0000 \u0000 </li>\u0000 </ol> The main way to prove these equivalences is by using the Quillen equivalences between quasi-categories and complete Segal spaces as defined by Joyal–Tierney and the straightening construction due to Lurie.</div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-021-00288-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4780757","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: 7

A cochain level proof of Adem relations in the mod 2 Steenrod algebra mod2 Steenrod代数中Adem关系的协链水平证明

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2021-08-19 DOI: 10.1007/s40062-021-00287-3

Greg Brumfiel, Anibal Medina-Mardones, John Morgan

引用次数: 9

Relative singularity categories and singular equivalences 相对奇异范畴和奇异等价

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2021-08-18 DOI: 10.1007/s40062-021-00289-1

Rasool Hafezi

引用次数: 0

The equivalence between Feynman transform and Verdier duality 费曼变换与维迪尔对偶的等价性

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2021-07-23 DOI: 10.1007/s40062-021-00286-4

Hao Yu

{"title":"The equivalence between Feynman transform and Verdier duality","authors":"Hao Yu","doi":"10.1007/s40062-021-00286-4","DOIUrl":"10.1007/s40062-021-00286-4","url":null,"abstract":"<div>The equivalence between dg duality and Verdier duality has been established for cyclic operads earlier. We propose a generalization of this correspondence from cyclic operads and dg duality to twisted modular operads and the Feynman transform. Specifically, for each twisted modular operad (mathcal {P}) (taking values in dg-vector spaces over a field k of characteristic 0), there is a certain sheaf (mathcal {F}) associated with it on the moduli space of stable metric graphs such that the Verdier dual sheaf (Dmathcal {F}) is associated with the Feynman transform (Fmathcal {P}) of (mathcal {P}). In the course of the proof, we also prove a relation between cyclic operads and modular operads originally proposed in the pioneering work of Getzler and Kapranov; however, to the best knowledge of the author, no proof has appeared. This geometric interpretation in operad theory is of fundamental importance. We believe this result will illuminate many aspects of the theory of modular operads and find many applications in the future. We illustrate an application of this result, giving another proof on the homotopy properties of the Feynman transform, which is quite intuitive and simpler than the original proof.</div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-021-00286-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4893099","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 K(1)-local homotopy of (mathrm {tmf}wedge mathrm {tmf}) 的K(1)-局部同伦 (mathrm {tmf}wedge mathrm {tmf})

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2021-07-20 DOI: 10.1007/s40062-021-00283-7

Dominic Leon Culver, Paul VanKoughnett

引用次数: 0

2-Segal objects and algebras in spans 跨度中的2-分段对象和代数

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2021-05-17 DOI: 10.1007/s40062-021-00282-8

Walker H. Stern

引用次数: 6

Torsion in the magnitude homology of graphs 图的大小同调中的扭转

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2021-05-15 DOI: 10.1007/s40062-021-00281-9

Radmila Sazdanovic, Victor Summers

引用次数: 8

Derived categories of NDG categories NDG类别的衍生类别

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2021-03-31 DOI: 10.1007/s40062-021-00279-3

Jun-ichi Miyachi, Hiroshi Nagase

引用次数: 0

On the relative K-group in the ETNC, Part II 论etc中的相对k群，第二部分

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2020-11-06 DOI: 10.1007/s40062-020-00267-z

Oliver Braunling

引用次数: 0