Smooth free involution of HCP3 and Smith conjecture for imbeddings of S-3 in S-6

doi:10.1007/s00208-007-0134-y

	Smooth free involution of HCP3 and Smith conjecture for imbeddings of S-3 in S-6
	Li, Bang-He ; Lue, Zhi
刊名	MATHEMATISCHE ANNALEN
	2007-12-01
卷号	339 期号:4 页码:879-889
ISSN号	0025-5831
DOI	10.1007/s00208-007-0134-y
英文摘要	This paper establishes an equivalence between existence of free involutions on HCP3 and existence of involutions on S-6 with fixed point set an imbedded S-3, then a family of counterexamples of the Smith conjecture for imbeddings of S-3 in S-6 are given by known result on HCP3. In addition, this paper also shows that every smooth homotopy complex projective three-space admits no orientation preserving smooth free involution, which answers an open problem ( Petrie T in Lecture Notes in Mathematics, Springer, New York, Vol. 298, pp. 234 - 259, 1972). Moreover, the study of existence problem for smooth orientation preserving involutions on HCP3 is completed.
WOS研究方向	Mathematics
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000249652700008
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/4106]
专题	中国科学院数学与系统科学研究院
通讯作者	Lue, Zhi
作者单位	1.Fudan Univ, Sch Math Sci, Inst Math, Shanghai 200433, Peoples R China 2.Acad Sinica, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Li, Bang-He,Lue, Zhi. Smooth free involution of HCP3 and Smith conjecture for imbeddings of S-3 in S-6[J]. MATHEMATISCHE ANNALEN,2007,339(4):879-889.
APA	Li, Bang-He,&Lue, Zhi.(2007).Smooth free involution of HCP3 and Smith conjecture for imbeddings of S-3 in S-6.MATHEMATISCHE ANNALEN,339(4),879-889.
MLA	Li, Bang-He,et al."Smooth free involution of HCP3 and Smith conjecture for imbeddings of S-3 in S-6".MATHEMATISCHE ANNALEN 339.4(2007):879-889.