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

利用传递图研究束的几何性质及其应用

• 批准号: 10640080
• 负责人: IMAOKA Mitsunori
• 金额: $ 0.96万
• 依托单位: Hiroshima University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640080/
• 关键词: transfer maps; sphere bundles; characteristic classes; projective spaces; homotopy; cohomology; ファイバーバンドル; ホモロジー

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.

本文主要研究球丛上的转移映射，重点是：推广了投射空间上转移映射的有效性，并将其结果应用于各种球丛的研究，得到了如下结果：1.通过用一些Thom空间表示转移映射的上纤维，阐明了计算转移映射的e-不变量的方法，推广了与射影空间有关的转移映射的一些结果.分析了向量丛稳定等价于线丛之和的情形。在这种情况下，e-不变量可以用一些组合数学来表示。我们应用各种转移映射研究了球面稳定同伦群中元素的加框超曲面表示，我们的结果已发表在M。Imaoka和K .库瓦纳：四元数射影空间上的稳定可扩向量丛，广岛数学杂志29（1999），273- 279. M. Imaoka和K.克纳普：球丛的转移映射，数学会志，日本，52（2000），印刷中。

项目成果

Mitsunori Imaoka: "Transfer maps of sphere bundles"Journal of the Mathematical Society of Japan. 52 (in print). (2000)

Mitsunori Imaoka：“球束的传递图”日本数学会杂志。

Teiichi Kobayashi: "Stably extendible vector bundles over the real projective spaces and the lens spaces"Hiroshima Mathematical Journal. 29. 631-638 (1999)

Teiichi Kobayashi：“在实射影空间和透镜空间上稳定可扩展的向量束”广岛数学杂志。

Teiichi Kobayashi: "Stably extendible vector bundles over the real projective spaces and the lens spaces"Hiroshima Mathematical Joutnal. 29・3. 631-638 (1999)

Teiichi Kobayashi：“实射影空间和透镜空间上的稳定可扩展向量束”广岛数学杂志 29・3（1999）。

Teiichi Kobayashi: "Steble extendibility of normal bundles associated to immersions of real projective spaces and lens spaces"Mem.Fac.Sci.Kochi Univ.Ser.A Math.. 21. 31-38 (2000)

Teiichi Kobayashi：“与真实射影空间和透镜空间的浸没相关的法向丛的稳定可扩展性”Mem.Fac.Sci.Kochi Univ.Ser.A Math.. 21. 31-38 (2000)

Mitsunori Imaoka: "Stably extendible vector bundles over the quaternionic projective spaces" Hiroshima Mathematical Journal. 29・1 or 2(予定). (1999)

Mitsunori Imaoka：“四元射影空间上的稳定可扩展向量丛”广岛数学杂志 29・1 或 2（计划）。