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Combinatorial k-systoles on a punctured torus and a pair of pants 组合k型收缩压在穿孔的环体和一条裤子上
Confluentes Mathematici Pub Date : 2021-08-18 DOI: 10.5802/cml.76
ElHadji Abdou Aziz Diop, Masseye Gaye, Abdoul Karim Sane
{"title":"Combinatorial k-systoles on a punctured torus and a pair of pants","authors":"ElHadji Abdou Aziz Diop, Masseye Gaye, Abdoul Karim Sane","doi":"10.5802/cml.76","DOIUrl":"https://doi.org/10.5802/cml.76","url":null,"abstract":"In this paper S denotes a surface homeomorphic to a punctured torus or a pair of pants. Our interest is the study of combinatorial k-systoles, that is closed curves with self-intersection numbers greater than k and with least combinatorial length. We show that the maximal intersection number Ic k of combinatorial k-systoles of S grows like k and lim sup k→+∞ (Ic k − k) = +∞. This result, in case of a pair of pants and a punctured torus, is a positive response to the combinatorial version of the Erlandsson-Parlier conjecture, originally formulated for the geometric length.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"145 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80501330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A priori and a posteriori error analysis for a hybrid formulation of a prestressed shell model. 预应力壳模型混合公式的先验和后验误差分析。
Confluentes Mathematici Pub Date : 2021-03-22 DOI: 10.22541/AU.161639868.88765742/V1
S. Nicaise, I. Merabet, Bara Rr
{"title":"A priori and a posteriori error analysis for a hybrid formulation of a prestressed shell model.","authors":"S. Nicaise, I. Merabet, Bara Rr","doi":"10.22541/AU.161639868.88765742/V1","DOIUrl":"https://doi.org/10.22541/AU.161639868.88765742/V1","url":null,"abstract":"This work deals with the finite element approximation of a prestressed\u0000shell model using a new formulation where the unknowns (the displacement\u0000and the rotation of fibers normal to the midsurface) are described in\u0000Cartesian and local covariant basis respectively. Due to the constraint\u0000involved in the definition of the functional space, a penalized version\u0000is then considered. We obtain a non robust a priori error estimate of\u0000this penalized formulation, but a robust one is obtained for its mixed\u0000formulation. Moreover, we present a reliable and efficient a posteriori\u0000error estimator of the penalized formulation. Numerical tests are\u0000included that confirmthe efficiency of our residual a posteriori\u0000estimator.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"312 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89957084","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Iterated Brownian motion ad libitum is not the pseudo-arc 任意迭代布朗运动不是伪弧
Confluentes Mathematici Pub Date : 2021-01-29 DOI: 10.5802/cml.70
Jérôme Casse, N. Curien
{"title":"Iterated Brownian motion ad libitum is not the pseudo-arc","authors":"Jérôme Casse, N. Curien","doi":"10.5802/cml.70","DOIUrl":"https://doi.org/10.5802/cml.70","url":null,"abstract":"We show that the construction of a random continuum $mathcal{C}$ from independent two-sided Brownian motions as considered in arXiv:2004.01367 almost surely yields a non-degenerate indecomposable but not-hereditary indecomposable continuum. In particular $mathcal{C}$ is (unfortunately) not the pseudo-arc.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89505098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Epimorphism testing with virtually Abelian targets 具有虚拟阿贝尔目标的上射检验
Confluentes Mathematici Pub Date : 2020-10-15 DOI: 10.5802/cml.72
Stefan Friedl, C. Loeh
{"title":"Epimorphism testing with virtually Abelian targets","authors":"Stefan Friedl, C. Loeh","doi":"10.5802/cml.72","DOIUrl":"https://doi.org/10.5802/cml.72","url":null,"abstract":"We show that the epimorphism problem is solvable for targets that are virtually cyclic or a product of an Abelian group and a finite group.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"168 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74908068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Slope filtrations: Erratum 斜坡过滤:勘误
Confluentes Mathematici Pub Date : 2020-09-25 DOI: 10.5802/CML.64
Y. Andre
{"title":"Slope filtrations: Erratum","authors":"Y. Andre","doi":"10.5802/CML.64","DOIUrl":"https://doi.org/10.5802/CML.64","url":null,"abstract":"Erratum for the paper “Slope Filtrations”, Confluentes Mathematici, Vol. 1, No. 1 (2009) 1–85 (1) Example 1.2.2.(2): actually, the usual orthogonal sum is neither a coproduct (nor a product), and in fact, the category of hermitian spaces does not admit finite coproducts (this is not used elsewhere). (2) Discard Lemma 1.2.8 and the undefined notion of “refinement\", which are used only in Proposition 1.4.18. Replace the given proof of Proposition 1.4.18 by the following: Proof. — It suffices to show (by induction on rk N) that for any strict subobject N ofM , the point (rk N, deg N) lies below NP (M). If i denotes the minimal index such that N is contained in the notch Mi of the flag F(M), this amounts to: deg N 6 degMi−1 + λi(rkN − rkMi−1). Let p : N ↪→ Mi → Mi/Mi−1 be the composed morphism. Since Mi/Mi−1 is semistable of slope λi and N/(N ∩Mi−1)→ Imp is epi-monic, one has μ(N/(N∩Mi−1)) 6 λi. By additivity of rk and deg in the sequence 0→ (N ∩Mi−1)→ N → N/(N ∩Mi−1)→ 0, one gets degN 6 λi(rkN − rk(N ∩Mi−1)) + deg(N ∩Mi−1). On the other hand, by induction, the point (rk (N ∩Mi−1),deg (N ∩Mi−1)) lies below NP (M), which implies that deg(N ∩Mi−1) 6 degMi−1 − λi(rkMi−1 − rk(N ∩Mi−1)). By combining the last two inequalities, one gets deg N 6 degMi−1 + λi(rkN − rkMi−1) as wanted. (3) In Lemma 1.2.18, replace the sum N+P in the sense of Section 1.2.3, which is the image of N ⊕P → Q, by the coimage of this morphism (which is the usual sum of N and P in the abelian envelop A). This lemma is not used elsewhere in the paper.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"30 1","pages":"147-148"},"PeriodicalIF":0.0,"publicationDate":"2020-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86001630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Unitary representations of p-adic U(5) p进U(5)的酉表示
Confluentes Mathematici Pub Date : 2020-09-25 DOI: 10.5802/CML.63
Claudia Schoemann
{"title":"Unitary representations of p-adic U(5)","authors":"Claudia Schoemann","doi":"10.5802/CML.63","DOIUrl":"https://doi.org/10.5802/CML.63","url":null,"abstract":"","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"145 1","pages":"93-146"},"PeriodicalIF":0.0,"publicationDate":"2020-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86216119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Properties expressible in small fragments of the theory of the hyperfinite II 1 factor 在超有限因子理论的小片段中可表达的性质
Confluentes Mathematici Pub Date : 2020-07-22 DOI: 10.5802/CML.67
Isaac Goldbring, B. Hart
{"title":"Properties expressible in small fragments of the theory of the hyperfinite II 1 factor","authors":"Isaac Goldbring, B. Hart","doi":"10.5802/CML.67","DOIUrl":"https://doi.org/10.5802/CML.67","url":null,"abstract":"We show that any II$_1$ factor that has the same 4-quantifier theory as the hyperfinite II$_1$ factor $mathcal{R}$ satisfies the conclusion of the Popa Factorial Commutant Embedding Problem (FCEP) and has the Brown property. These results improve recent results proving the same conclusions under the stronger assumption that the factor is actually elementarily equivalent to $mathcal{R}$. In the same spirit, we improve a recent result of the first-named author, who showed that if (1) the amalgamated free product of embeddable factors over a property (T) base is once again embeddable, and (2) $mathcal{R}$ is an infinitely generic embeddable factor, then the FCEP is true of all property (T) factors. In this paper, it is shown that item (2) can be weakened to assume that $mathcal{R}$ has the same 3-quantifier theory as an infinitely generic embeddable factor.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"97 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90627006","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Introduction to a small cancellation theorem 一个小消去定理的介绍
Confluentes Mathematici Pub Date : 2020-05-12 DOI: 10.5802/cml.73
St'ephane Lamy, Anne Lonjou
{"title":"Introduction to a small cancellation theorem","authors":"St'ephane Lamy, Anne Lonjou","doi":"10.5802/cml.73","DOIUrl":"https://doi.org/10.5802/cml.73","url":null,"abstract":"This note is intended as an introduction to two previous works respectively by Dahmani, Guirardel, Osin, and by Cantat, Lamy. We give two proofs of a Small Cancellation Theorem for groups acting on a simplicial tree. We discuss the application to the group of plane polynomial automorphisms over any ground field.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76005595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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 solutions of the universal differential equation with three regular singularities (On solutions of KZ 3 ) 关于具有三个正则奇点的通用微分方程的解(关于kz3的解)
Confluentes Mathematici Pub Date : 2020-03-09 DOI: 10.5802/cml.59
V. H. N. Minh
{"title":"On the solutions of the universal differential equation with three regular singularities (On solutions of KZ 3 )","authors":"V. H. N. Minh","doi":"10.5802/cml.59","DOIUrl":"https://doi.org/10.5802/cml.59","url":null,"abstract":"This review concerns the resolution of a special case of Knizhnik-Zamolodchikov equations (KZ3) and our recent results on combinatorial aspects of zeta functions on several variables. In particular, we describe the action of the differential Galois group of KZ3 on the asymptotic expansions of its solutions leading to a group of associators which contains the unique Drinfel’d associator (or Drinfel’d series). Non trivial expressions of an associator with rational coefficients are also explicitly provided, based on the algebraic structure and the singularity analysis of the multi-indexed polylogarithms and harmonic sums.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"1 1","pages":"25-64"},"PeriodicalIF":0.0,"publicationDate":"2020-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87217570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
The model theory of Cohen rings 科恩的模型理论
Confluentes Mathematici Pub Date : 2019-04-17 DOI: 10.5802/cml.84
Sylvy Anscombe, Franziska Jahnke
{"title":"The model theory of Cohen rings","authors":"Sylvy Anscombe, Franziska Jahnke","doi":"10.5802/cml.84","DOIUrl":"https://doi.org/10.5802/cml.84","url":null,"abstract":"The aim of this article is to give a self-contained account of the algebra and model theory of Cohen rings, a natural generalization of Witt rings. Witt rings are only valuation rings in case the residue field is perfect, and Cohen rings arise as the Witt ring analogon over imperfect residue fields. Just as one studies truncated Witt rings to understand Witt rings, we study Cohen rings of positive characteristic as well as of characteristic zero.Our main results are a relative completeness and a relative model completeness result for Cohen rings, which imply the corresponding Ax–Kochen/Ershov type results for unramified henselian valued fields also in case the residue field is imperfect. The key to these results is a proof of relative quantifier elimination down to the residue field in an appropriate language which holds in any unramified henselian valued field","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88548713","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
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