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On malnormal peripheral subgroups of the fundamental group of a $3$-manifold $3$-流形基群的非正常外周子群
Confluentes Mathematici Pub Date : 2014-01-01 DOI: 10.5802/CML.12
P. Harpe, Claude Weber
{"title":"On malnormal peripheral subgroups of the fundamental group of a $3$-manifold","authors":"P. Harpe, Claude Weber","doi":"10.5802/CML.12","DOIUrl":"https://doi.org/10.5802/CML.12","url":null,"abstract":"Let K be a non-trivial knot in the 3-sphere, EK its exterior, GK = π1(EK) its group, and PK = π1(∂EK) ⊂ GK its peripheral subgroup. We show that PK is malnormal in GK , namely that gPKg ∩ PK = {e} for any g ∈ GK with g / ∈ PK , unless K is in one of the following three classes: torus knots, cable knots, and composite knots; these are exactly the classes for which there exist annuli in EK attached to TK which are not boundary parallel (Theorem 1 and Corollary 2). More generally, we characterise malnormal peripheral subgroups in the fundamental group of a compact orientable irreducible 3-manifold of which the boundary is a non-empty union of tori (Theorem 3). Proofs are written with non-expert readers in mind. Half of our paper (Appendices A to D) is a reminder of some three-manifold topology as it flourished before the Thurston revolution. In a companion paper [15], we collect general facts on malnormal subgroups and Frobenius groups, and we review a number of examples.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"2 1","pages":"41-64"},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89914975","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: 7
Malnormal subgroups and Frobenius groups: basics and examples 非正常子群和Frobenius群:基础和例子
Confluentes Mathematici Pub Date : 2014-01-01 DOI: 10.5802/CML.13
P. Harpe, Claude Weber
{"title":"Malnormal subgroups and Frobenius groups: basics and examples","authors":"P. Harpe, Claude Weber","doi":"10.5802/CML.13","DOIUrl":"https://doi.org/10.5802/CML.13","url":null,"abstract":"Malnormal subgroups occur in various contexts. We review a large number of examples, and compare the general situation to that of finite Frobenius groups of permutations. In a companion paper [18], we analyse when peripheral subgroups of knot groups and 3-manifold groups are malnormal.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"183 1","pages":"65-76"},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74870386","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: 19
Ergodic Dilation of a Quantum Dynamical System 量子动力系统的遍历膨胀
Confluentes Mathematici Pub Date : 2014-01-01 DOI: 10.5802/CML.14
Carlo Pandiscia
{"title":"Ergodic Dilation of a Quantum Dynamical System","authors":"Carlo Pandiscia","doi":"10.5802/CML.14","DOIUrl":"https://doi.org/10.5802/CML.14","url":null,"abstract":". Using the Nagy dilation of linear contractions on Hilbert space and the Stinespring’s theorem for completely positive maps, we prove that any quantum dynamical system admits a dilation in the sense of Muhly and Solel which satisfies the same ergodic properties of the original quantum dynamical system.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"13 1","pages":"77-91"},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81938802","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: 3
Espaces de Berkovich, polytopes, squelettes et théorie des modèles : erratum 伯克维奇空间，多面体，骨骼和模型理论:勘误表
Confluentes Mathematici Pub Date : 2013-01-01 DOI: 10.5802/CML.7
A. Ducros
{"title":"Espaces de Berkovich, polytopes, squelettes et théorie des modèles : erratum","authors":"A. Ducros","doi":"10.5802/CML.7","DOIUrl":"https://doi.org/10.5802/CML.7","url":null,"abstract":"L’accès aux articles de la revue « Confluentes Mathematici » (http://cml.cedram.org/), implique l’accord avec les conditions générales d’utilisation (http://cml.cedram.org/legal/). Toute reproduction en tout ou partie de cet article sous quelque forme que ce soit pour tout usage autre que l’utilisation á fin strictement personnelle du copiste est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"1014 1","pages":"43-44"},"PeriodicalIF":0.0,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77174649","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
Exponentiations over the quantum algebra $U_{q}(sl_2(mathbb{C}))$ 量子代数$U_{q}(sl_2(mathbb{C}))$的幂次
Confluentes Mathematici Pub Date : 2013-01-01 DOI: 10.5802/cml.8
Sonia L'Innocente, Françoise Point, C. Toffalori
{"title":"Exponentiations over the quantum algebra $U_{q}(sl_2(mathbb{C}))$","authors":"Sonia L'Innocente, Françoise Point, C. Toffalori","doi":"10.5802/cml.8","DOIUrl":"https://doi.org/10.5802/cml.8","url":null,"abstract":"","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"8 1","pages":"45-69"},"PeriodicalIF":0.0,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83415908","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
Entre géométrie et théorie des substitutions : une étude de cas autour des vingt-sept droites d’une surface cubique 在几何学和替换理论之间:一个关于立方体曲面的27条直线的案例研究
Confluentes Mathematici Pub Date : 2013-01-01 DOI: 10.5802/CML.2
François Lê
{"title":"Entre géométrie et théorie des substitutions : une étude de cas autour des vingt-sept droites d’une surface cubique","authors":"François Lê","doi":"10.5802/CML.2","DOIUrl":"https://doi.org/10.5802/CML.2","url":null,"abstract":"L’acces aux articles de la revue « Confluentes Mathematici » (http://cml.cedram.org/), implique l’accord avec les conditions generales d’utilisation (http://cml.cedram.org/legal/). Toute reproduction en tout ou partie de cet article sous quelque forme que ce soit pour tout usage autre que l’utilisation a fin strictement personnelle du copiste est constitutive d’une infraction penale. Toute copie ou impression de ce fichier doit contenir la presente mention de copyright.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"61 1","pages":"23-71"},"PeriodicalIF":0.0,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77034179","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: 9
Finite Groups with some $s$-Permutably Embedded and Weakly $s$-Permutable Subgroups 具有$s$-可置换嵌入和弱$s$-可置换子群的有限群
Confluentes Mathematici Pub Date : 2013-01-01 DOI: 10.5802/cml.4
Fenfang Xie, Jinjin Wang, Jiayi Xia, Guolei Zhong
{"title":"Finite Groups with some $s$-Permutably Embedded and Weakly $s$-Permutable Subgroups","authors":"Fenfang Xie, Jinjin Wang, Jiayi Xia, Guolei Zhong","doi":"10.5802/cml.4","DOIUrl":"https://doi.org/10.5802/cml.4","url":null,"abstract":"Let G be a finite group, p the smallest prime dividing the order of G and P a Sylow p-subgroup of G with the smallest generator number d. There is a set Md(P ) = {P1, P2, · · · , Pd} of maximal subgroups of P such that ⋂d i=1 Pi = Φ(P ). In the present paper, we investigate the structure of a finite group under the assumption that every member ofMd(P ) is either s-permutably embedded or weakly s-permutable in G to give criteria for a group to be p-supersolvable or p-nilpotent.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"103 1","pages":"93-100"},"PeriodicalIF":0.0,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85382402","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
INTERVAL EXCHANGE TRANSFORMATION EXTENSION OF A SUBSTITUTION DYNAMICAL SYSTEM 替换动力系统的区间交换变换扩展
Confluentes Mathematici Pub Date : 2012-12-01 DOI: 10.1142/S1793744212500053
X. Bressaud, Y. Jullian
{"title":"INTERVAL EXCHANGE TRANSFORMATION EXTENSION OF A SUBSTITUTION DYNAMICAL SYSTEM","authors":"X. Bressaud, Y. Jullian","doi":"10.1142/S1793744212500053","DOIUrl":"https://doi.org/10.1142/S1793744212500053","url":null,"abstract":"Let α be a free group automorphism on FN with maximal index and Σα the associated attracting subshift. We prove that there exists an Interval Exchange Transformation on the circle whose coding factorizes onto Σα. In the case when there is an explicit construction of the ℝ-tree associated to α, we construct algorithmically such IET. We conclude by giving examples.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"57 1","pages":"1250005"},"PeriodicalIF":0.0,"publicationDate":"2012-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73263269","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
Density of smooth maps for fractional Sobolev spaces $W^{s, p}$ into $ell$ simply connected manifolds when $s ge 1$ 分数Sobolev空间$W^{s, p}$到$ell$单连通流形的光滑映射密度
Confluentes Mathematici Pub Date : 2012-10-09 DOI: 10.5802/cml.5
P. Bousquet, A. Ponce, Jean Van Schaftingen
{"title":"Density of smooth maps for fractional Sobolev spaces $W^{s, p}$ into $ell$ simply connected manifolds when $s ge 1$","authors":"P. Bousquet, A. Ponce, Jean Van Schaftingen","doi":"10.5802/cml.5","DOIUrl":"https://doi.org/10.5802/cml.5","url":null,"abstract":"Given a compact manifold $N^n subset mathbb{R}^u$ and real numbers $s ge 1$ and $1 le p < infty$, we prove that the class $C^infty(overline{Q}^m; N^n)$ of smooth maps on the cube with values into $N^n$ is strongly dense in the fractional Sobolev space $W^{s, p}(Q^m; N^n)$ when $N^n$ is $lfloor sp floor$ simply connected. For $sp$ integer, we prove weak sequential density of $C^infty(overline{Q}^m; N^n)$ when $N^n$ is $sp - 1$ simply connected. The proofs are based on the existence of a retraction of $mathbb{^ u$ onto $N^n$ except for a small subset of $N^n$ and on a pointwise estimate of fractional derivatives of composition of maps in $W^{s, p} cap W^{1, sp}$.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"21 1","pages":"3-22"},"PeriodicalIF":0.0,"publicationDate":"2012-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87218992","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: 19
ON THE STEINHAUS AND BERGMAN PROPERTIES FOR INFINITE PRODUCTS OF FINITE GROUPS 有限群无穷积的steinhaus和bergman性质
Confluentes Mathematici Pub Date : 2012-09-27 DOI: 10.1142/S1793744212500028
S. Thomas, J. Zapletal
{"title":"ON THE STEINHAUS AND BERGMAN PROPERTIES FOR INFINITE PRODUCTS OF FINITE GROUPS","authors":"S. Thomas, J. Zapletal","doi":"10.1142/S1793744212500028","DOIUrl":"https://doi.org/10.1142/S1793744212500028","url":null,"abstract":"We study the relationship between the existence of nonprincipal ultrafilters over ω and the failure of the automatic continuity, Steinhaus and Bergman properties for infinite products of finite groups.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"20 4-6 1","pages":"1250002"},"PeriodicalIF":0.0,"publicationDate":"2012-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86566315","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: 7
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