M-纤维式同伦扩张性质及其应用  

M-Fibresise Homotopy Extension Property and Its Applications

作　　者：郑芳婷[1] 赵浩[1] 

机构地区：[1]华南师范大学数学科学学院,广州510631

出　　处：《华南师范大学学报（自然科学版）》2014年第3期18-24,共7页Journal of South China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11101161);教育部博士点基金新教师类项目(20114407120011)

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,这个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.Some homotopy 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 Mfibrewise 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.

关 键 词：拓扑范畴 M-纤维式范畴 同伦扩张 

分 类 号：O189.23[理学—数学]