Pub Date : 2021-11-11DOI: 10.1017/s1446788720000361
{"title":"JAZ volume 111 issue 3 Cover and Back matter","authors":"","doi":"10.1017/s1446788720000361","DOIUrl":"https://doi.org/10.1017/s1446788720000361","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"342 1","pages":"b1 - b3"},"PeriodicalIF":0.7,"publicationDate":"2021-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76600456","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}
Pub Date : 2021-11-11DOI: 10.1017/s1446788720000245
{"title":"INDEX","authors":"","doi":"10.1017/s1446788720000245","DOIUrl":"https://doi.org/10.1017/s1446788720000245","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"1125 1","pages":"430 - 431"},"PeriodicalIF":0.7,"publicationDate":"2021-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76803802","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}
Pub Date : 2021-11-11DOI: 10.1017/s144678872000035x
{"title":"JAZ volume 111 issue 3 Cover and Front matter","authors":"","doi":"10.1017/s144678872000035x","DOIUrl":"https://doi.org/10.1017/s144678872000035x","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"132 1","pages":"f1 - f2"},"PeriodicalIF":0.7,"publicationDate":"2021-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73012993","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}
Pub Date : 2021-11-08DOI: 10.1017/S1446788722000106
Francesco Fournier-Facio, C. Loeh, M. Moraschini
Abstract A group is boundedly acyclic if its bounded cohomology with trivial real coefficients vanishes in all positive degrees. Amenable groups are boundedly acyclic, while the first nonamenable examples are the group of compactly supported homeomorphisms of $ {mathbb {R}}^{n}$ (Matsumoto–Morita) and mitotic groups (Löh). We prove that binate (alias pseudo-mitotic) groups are boundedly acyclic, which provides a unifying approach to the aforementioned results. Moreover, we show that binate groups are universally boundedly acyclic. We obtain several new examples of boundedly acyclic groups as well as computations of the bounded cohomology of certain groups acting on the circle. In particular, we discuss how these results suggest that the bounded cohomology of the Thompson groups F, T, and V is as simple as possible.
{"title":"BOUNDED COHOMOLOGY AND BINATE GROUPS","authors":"Francesco Fournier-Facio, C. Loeh, M. Moraschini","doi":"10.1017/S1446788722000106","DOIUrl":"https://doi.org/10.1017/S1446788722000106","url":null,"abstract":"Abstract A group is boundedly acyclic if its bounded cohomology with trivial real coefficients vanishes in all positive degrees. Amenable groups are boundedly acyclic, while the first nonamenable examples are the group of compactly supported homeomorphisms of \u0000$ {mathbb {R}}^{n}$\u0000 (Matsumoto–Morita) and mitotic groups (Löh). We prove that binate (alias pseudo-mitotic) groups are boundedly acyclic, which provides a unifying approach to the aforementioned results. Moreover, we show that binate groups are universally boundedly acyclic. We obtain several new examples of boundedly acyclic groups as well as computations of the bounded cohomology of certain groups acting on the circle. In particular, we discuss how these results suggest that the bounded cohomology of the Thompson groups F, T, and V is as simple as possible.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"108 1","pages":"204 - 239"},"PeriodicalIF":0.7,"publicationDate":"2021-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87615331","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}
Pub Date : 2021-10-25DOI: 10.1017/S1446788721000161
S. A. Mutter
Abstract Using a result of Vdovina, we may associate to each complete connected bipartite graph $kappa $ a two-dimensional square complex, which we call a tile complex, whose link at each vertex is $kappa $ . We regard the tile complex in two different ways, each having a different structure as a $2$ -rank graph. To each $2$ -rank graph is associated a universal $C^{star }$ -algebra, for which we compute the K-theory, thus providing a new infinite collection of $2$ -rank graph algebras with explicit K-groups. We determine the homology of the tile complexes and give generalisations of the procedures to complexes and systems consisting of polygons with a higher number of sides.
{"title":"THE K-THEORY OF THE \u0000${mathit{C}}^{star }$\u0000 -ALGEBRAS OF 2-RANK GRAPHS ASSOCIATED TO COMPLETE BIPARTITE GRAPHS","authors":"S. A. Mutter","doi":"10.1017/S1446788721000161","DOIUrl":"https://doi.org/10.1017/S1446788721000161","url":null,"abstract":"Abstract Using a result of Vdovina, we may associate to each complete connected bipartite graph \u0000$kappa $\u0000 a two-dimensional square complex, which we call a tile complex, whose link at each vertex is \u0000$kappa $\u0000 . We regard the tile complex in two different ways, each having a different structure as a \u0000$2$\u0000 -rank graph. To each \u0000$2$\u0000 -rank graph is associated a universal \u0000$C^{star }$\u0000 -algebra, for which we compute the K-theory, thus providing a new infinite collection of \u0000$2$\u0000 -rank graph algebras with explicit K-groups. We determine the homology of the tile complexes and give generalisations of the procedures to complexes and systems consisting of polygons with a higher number of sides.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"19 1","pages":"119 - 144"},"PeriodicalIF":0.7,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82592811","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}
Pub Date : 2021-10-11DOI: 10.1017/S1446788721000173
Lingling Huang, Chao Ma
Abstract This paper is concerned with the growth rate of the product of consecutive partial quotients relative to the denominator of the convergent for the continued fraction expansion of an irrational number. More precisely, given a natural number $m,$ we determine the Hausdorff dimension of the following set: $$ begin{align*} E_m(tau)=bigg{xin [0,1): limsuplimits_{nrightarrowinfty}frac{log (a_n(x)a_{n+1}(x)cdots a_{n+m}(x))}{log q_n(x)}=taubigg}, end{align*} $$ where $tau $ is a nonnegative number. This extends the dimensional result of Dirichlet nonimprovable sets (when $m=1$ ) shown by Hussain, Kleinbock, Wadleigh and Wang.
{"title":"A DIMENSIONAL RESULT ON THE PRODUCT OF CONSECUTIVE PARTIAL QUOTIENTS IN CONTINUED FRACTIONS","authors":"Lingling Huang, Chao Ma","doi":"10.1017/S1446788721000173","DOIUrl":"https://doi.org/10.1017/S1446788721000173","url":null,"abstract":"Abstract This paper is concerned with the growth rate of the product of consecutive partial quotients relative to the denominator of the convergent for the continued fraction expansion of an irrational number. More precisely, given a natural number \u0000$m,$\u0000 we determine the Hausdorff dimension of the following set: \u0000$$ begin{align*} E_m(tau)=bigg{xin [0,1): limsuplimits_{nrightarrowinfty}frac{log (a_n(x)a_{n+1}(x)cdots a_{n+m}(x))}{log q_n(x)}=taubigg}, end{align*} $$\u0000 where \u0000$tau $\u0000 is a nonnegative number. This extends the dimensional result of Dirichlet nonimprovable sets (when \u0000$m=1$\u0000 ) shown by Hussain, Kleinbock, Wadleigh and Wang.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"75 4 1","pages":"357 - 385"},"PeriodicalIF":0.7,"publicationDate":"2021-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77315500","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}
Pub Date : 2021-10-01DOI: 10.1017/s1446788720000348
{"title":"JAZ volume 111 issue 2 Cover and Back matter","authors":"","doi":"10.1017/s1446788720000348","DOIUrl":"https://doi.org/10.1017/s1446788720000348","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"37 1","pages":"b1 - b2"},"PeriodicalIF":0.7,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81719744","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}
Pub Date : 2021-09-13DOI: 10.1017/s1446788720000336
{"title":"JAZ volume 111 issue 2 Cover and Front matter","authors":"","doi":"10.1017/s1446788720000336","DOIUrl":"https://doi.org/10.1017/s1446788720000336","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"22 1","pages":"f1 - f2"},"PeriodicalIF":0.7,"publicationDate":"2021-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75854384","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}
Pub Date : 2021-09-02DOI: 10.1017/S1446788722000167
Anthony Conway, D. Crowley, Mark Powell, Joerg Sixt
Abstract For every $k geq 2$ and $n geq 2$ , we construct n pairwise homotopically inequivalent simply connected, closed $4k$ -dimensional manifolds, all of which are stably diffeomorphic to one another. Each of these manifolds has hyperbolic intersection form and is stably parallelisable. In dimension four, we exhibit an analogous phenomenon for spin $^{c}$ structures on $S^2 times S^2$ . For $mgeq 1$ , we also provide similar $(4m-1)$ -connected $8m$ -dimensional examples, where the number of homotopy types in a stable diffeomorphism class is related to the order of the image of the stable J-homomorphism $pi _{4m-1}(SO) to pi ^s_{4m-1}$ .
摘要对于每一个$k geq 2$和$n geq 2$，我们构造了n个彼此稳定微分同构的对同伦不等价单连通闭$4k$维流形。这些流形均具有双曲交形式，且稳定平行。在四维中，我们展示了$S^2 times S^2$上的自旋$^{c}$结构的类似现象。对于$mgeq 1$，我们也提供了类似的$(4m-1)$连通$8m$维的例子，其中稳定的微分同态类中的同伦类型的数目与稳定的j同态$pi _{4m-1}(SO) to pi ^s_{4m-1}$的像的阶数有关。
{"title":"SIMPLY CONNECTED MANIFOLDS WITH LARGE HOMOTOPY STABLE CLASSES","authors":"Anthony Conway, D. Crowley, Mark Powell, Joerg Sixt","doi":"10.1017/S1446788722000167","DOIUrl":"https://doi.org/10.1017/S1446788722000167","url":null,"abstract":"Abstract For every \u0000$k geq 2$\u0000 and \u0000$n geq 2$\u0000 , we construct n pairwise homotopically inequivalent simply connected, closed \u0000$4k$\u0000 -dimensional manifolds, all of which are stably diffeomorphic to one another. Each of these manifolds has hyperbolic intersection form and is stably parallelisable. In dimension four, we exhibit an analogous phenomenon for spin \u0000$^{c}$\u0000 structures on \u0000$S^2 times S^2$\u0000 . For \u0000$mgeq 1$\u0000 , we also provide similar \u0000$(4m-1)$\u0000 -connected \u0000$8m$\u0000 -dimensional examples, where the number of homotopy types in a stable diffeomorphism class is related to the order of the image of the stable J-homomorphism \u0000$pi _{4m-1}(SO) to pi ^s_{4m-1}$\u0000 .","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"13 1","pages":"172 - 203"},"PeriodicalIF":0.7,"publicationDate":"2021-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78750642","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}
Pub Date : 2021-08-01DOI: 10.1017/s1446788720000324
{"title":"JAZ volume 111 issue 1 Cover and Back matter","authors":"","doi":"10.1017/s1446788720000324","DOIUrl":"https://doi.org/10.1017/s1446788720000324","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"28 1","pages":"b1 - b2"},"PeriodicalIF":0.7,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74002451","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}
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