Study on Geometrical properties of bundles using transfer maps and it's application

在这项研究中，我们发展了对球丛转移映射的研究，强调了以下几点：推广射影空间转移映射的有效性；应用这种转移映射的结果来研究各种丛。作为一些结果，我们得到了如下结果：1.通过用一些Thom空间来表示转移映射的余纤维，我们阐明了转移映射的e-不变量的计算方法，推广了关于射影空间转移映射的一些结果。我们分析了向量丛稳定等价于线丛和的情形。在这种情况下，e-不变量用一些组合子来表示。我们利用几种转移映射研究了球面稳定同伦群中的元素用框架超曲面表示的问题.我们的结果已经并将在M.Imaoka和K.Kuwana：四元数射影空间上的稳定可扩张向量丛，广岛数学。J·29(1999)，273-279 M.Imaoka和K.Knapp：球丛的转移映射，J.数学。SoC。《日本，52(2000)》，印刷本。

In this research, we have developed our study on transfer maps of sphere bundles with stressing the following points :To extend the efficiency of the transfer maps concerning projective spaces ; to apply the results of such transfer maps to investigate various bundles.As some of results, we have got the following :1. By representing the cofiber of the transfer maps using some Thom spaces, we clarified the methods of computing the e-invariants of the transfer maps, and extended some results for the transfer maps related to the projective spaces.2. We analyzed the cases when a vector bundle is stably equivalent to the sum of line bundles. In such cases the e-invariants are represented by using some combinatorics.3. We applied some sorts of transfer maps to the study on representing of elements in the stable homotopy groups of spheres by framed hypersurfaces.Our results appeared and will appear in :M. Imaoka and K . Kuwana : Stably extendible vector bundles over the quaternionic projective spaces, Hiroshima Math. J. 29(1999), 273-279.M. Imaoka and K. Knapp : Transfer maps of sphere bundles, J. Math. Soc. Japan, 52(2000), in print.