M-纤维式同伦扩张及其应用

郑芳婷, 赵浩

郑芳婷, 赵浩. M-纤维式同伦扩张及其应用[J]. 华南师范大学学报(自然科学版), 2014, 46(3).
引用本文: 郑芳婷, 赵浩. M-纤维式同伦扩张及其应用[J]. 华南师范大学学报(自然科学版), 2014, 46(3).
Fang-ting ZHENG, Hao ZHAO. M-fibrewise homotopy extension property and its applicationos[J]. Journal of South China Normal University (Natural Science Edition), 2014, 46(3).
Citation: Fang-ting ZHENG, Hao ZHAO. M-fibrewise homotopy extension property and its applicationos[J]. Journal of South China Normal University (Natural Science Edition), 2014, 46(3).

M-纤维式同伦扩张及其应用

基金项目: 

国家自然科学基金;教育部博士点基金新老师类项目

详细信息
    通讯作者:

    赵浩

M-fibrewise homotopy extension property and its applicationos

More Information
    Corresponding author:

    Hao ZHAO

  • 摘要: 着重研究了M-纤维式范畴中的同伦论相关概念, 即M-纤维式同伦扩张性质. 通过M-纤维式收缩以及M-纤维式形变收缩的概念,给出了M-纤维式同伦扩张性质的等价描述,从而推广了一般拓扑范畴中同伦扩张性质的相关等价描述. 另外,证明了在M-纤维式范畴中的一些空间构造,如M-纤维式贴附空间的同伦不变形性. 最后, 对于2个M-纤维式映射是否同伦等价的问题,通过M-纤维式映射柱的概念给出了相关的判定定理,这一判定是一般拓扑范畴中两映射是否同伦等价的判定的自然推广.
    Abstract: Some homotopical notions in M-fibrewise category such as M-fibrewise homotopy extension property are studied. With the help of notions such as M-fibreswise retract and M-fibrewise deformation retract, an equivalent description of M-fibrewise homotopy extension property which generalizes the related one for homotopy extension property in general topological category is given. Furthermore the homotopy invariance of some constructions in M-fibrewise category such as M-fibrewise attaching space is shown. Finally, a judgment theorem is given via M-fibrewise mapping cylinder for the problem on whether two M-fibrewise maps are homotopic. This judgment is a natural generalization for the one on whether two maps are homotopic in general topological category.
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出版历程
  • 收稿日期:  2013-09-23
  • 修回日期:  2014-02-14
  • 刊出日期:  2014-05-24

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