{"title":"束的可定向性:阻碍理论及其在k理论中的应用","authors":"Yuli B. Rudyak","doi":"10.1070/SM1991V068N02ABEH001934","DOIUrl":null,"url":null,"abstract":"An obstruction theory is constructed for orientability of vector, piecewise-linear, and topological Rn-bundles and homotopy sphere bundles (spherical fibrations) in generalized cohomology theories. The results are applied to study the orientability of bundles in complex K-theory. In particular, it turns out that the problem of K-orientability for each of the four classes of bundles mentioned above is to be solved differently. Bibliography: 20 titles.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"3 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1991-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"ORIENTABILITY OF BUNDLES: OBSTRUCTION THEORY AND APPLICATIONS TO K-THEORY\",\"authors\":\"Yuli B. Rudyak\",\"doi\":\"10.1070/SM1991V068N02ABEH001934\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"An obstruction theory is constructed for orientability of vector, piecewise-linear, and topological Rn-bundles and homotopy sphere bundles (spherical fibrations) in generalized cohomology theories. The results are applied to study the orientability of bundles in complex K-theory. In particular, it turns out that the problem of K-orientability for each of the four classes of bundles mentioned above is to be solved differently. Bibliography: 20 titles.\",\"PeriodicalId\":208776,\"journal\":{\"name\":\"Mathematics of The Ussr-sbornik\",\"volume\":\"3 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1991-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics of The Ussr-sbornik\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1070/SM1991V068N02ABEH001934\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of The Ussr-sbornik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/SM1991V068N02ABEH001934","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
ORIENTABILITY OF BUNDLES: OBSTRUCTION THEORY AND APPLICATIONS TO K-THEORY
An obstruction theory is constructed for orientability of vector, piecewise-linear, and topological Rn-bundles and homotopy sphere bundles (spherical fibrations) in generalized cohomology theories. The results are applied to study the orientability of bundles in complex K-theory. In particular, it turns out that the problem of K-orientability for each of the four classes of bundles mentioned above is to be solved differently. Bibliography: 20 titles.
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