{"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":null,"pages":null},"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}
Anthony Conway, D. Crowley, Mark Powell, Joerg Sixt
{"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":null,"pages":null},"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}
{"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":null,"pages":null},"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}
{"title":"JAZ volume 111 issue 1 Cover and Front matter","authors":"","doi":"10.1017/s1446788720000312","DOIUrl":"https://doi.org/10.1017/s1446788720000312","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84417652","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}
{"title":"GHOSTS AND CONGRUENCES FOR -APPROXIMATIONS OF HYPERGEOMETRIC PERIODS","authors":"A. Varchenko, W. Zudilin","doi":"10.1017/S1446788723000083","DOIUrl":"https://doi.org/10.1017/S1446788723000083","url":null,"abstract":"\u0000 We prove general Dwork-type congruences for constant terms attached to tuples of Laurent polynomials. We apply this result to establishing arithmetic and p-adic analytic properties of functions originating from polynomial solutions modulo \u0000 \u0000 \u0000 \u0000$p^s$\u0000\u0000 \u0000 of hypergeometric and Knizhnik–Zamolodchikov (KZ) equations, solutions which come as coefficients of master polynomials and whose coefficients are integers. As an application, we show that the simplest example of a p-adic KZ connection has an invariant line subbundle while its complex analog has no nontrivial subbundles due to the irreducibility of its monodromy representation.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87332550","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}
{"title":"SOME \u0000$boldsymbol {L^p}$\u0000 -HARDY AND \u0000$boldsymbol {L^p}$\u0000 -RELLICH TYPE INEQUALITIES WITH REMAINDER TERMS","authors":"Yongyang Jin, Shoufeng Shen","doi":"10.1017/S1446788721000100","DOIUrl":"https://doi.org/10.1017/S1446788721000100","url":null,"abstract":"Abstract In this paper we obtain some improved \u0000$L^p$\u0000 -Hardy and \u0000$L^p$\u0000 -Rellich inequalities on bounded domains of Riemannian manifolds. For Cartan–Hadamard manifolds we prove the inequalities with sharp constants and with weights being hyperbolic functions of the Riemannian distance.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86688076","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}