{"title":"一类流形的浸没问题","authors":"Teiichi Kobayashi","doi":"10.32917/HMJ/1206138968","DOIUrl":null,"url":null,"abstract":"In this note, let M denote a compact connected orientable C°°-manifold (with boundary) of dimension m, and R the A -dimensional Euclidean space. We write M^R (or MΦR) to denote the existence (or the non-existence) of a C°°-immersion of M into R. The purpose of this note is to discuss the immersion problem for some manifolds M whose integral cohomology groups H\\M; Z) in positive dimensions are finite and have no 2-primary subgroups. We obtain the following immersion theorems of such manifolds M into R\\ where h is near to 3m/2.","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"54 4 1","pages":"161-171"},"PeriodicalIF":0.0000,"publicationDate":"1967-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the immersion problem for certain manifolds\",\"authors\":\"Teiichi Kobayashi\",\"doi\":\"10.32917/HMJ/1206138968\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this note, let M denote a compact connected orientable C°°-manifold (with boundary) of dimension m, and R the A -dimensional Euclidean space. We write M^R (or MΦR) to denote the existence (or the non-existence) of a C°°-immersion of M into R. The purpose of this note is to discuss the immersion problem for some manifolds M whose integral cohomology groups H\\\\M; Z) in positive dimensions are finite and have no 2-primary subgroups. We obtain the following immersion theorems of such manifolds M into R\\\\ where h is near to 3m/2.\",\"PeriodicalId\":17080,\"journal\":{\"name\":\"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry\",\"volume\":\"54 4 1\",\"pages\":\"161-171\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1967-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.32917/HMJ/1206138968\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.32917/HMJ/1206138968","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this note, let M denote a compact connected orientable C°°-manifold (with boundary) of dimension m, and R the A -dimensional Euclidean space. We write M^R (or MΦR) to denote the existence (or the non-existence) of a C°°-immersion of M into R. The purpose of this note is to discuss the immersion problem for some manifolds M whose integral cohomology groups H\M; Z) in positive dimensions are finite and have no 2-primary subgroups. We obtain the following immersion theorems of such manifolds M into R\ where h is near to 3m/2.