Secondary Brown-Kervaire quadratic forms and pi-manifolds

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	Secondary Brown-Kervaire quadratic forms and pi-manifolds
	Fang, FQ ; Pan, JZ
	2004
发表期刊	FORUM MATHEMATICUM
ISSN	0933-7741
卷号	16 期号:4 页码:459-481
摘要	Given a Phi-oriented manifold (cf. Definition 1.1) M of dimension 2n, where n greater than or equal to 4 and n not equal 3 (mod 4), we prove that there is a quadratic function phi(M) : Hn-1 (M, Z(4)) --> Q/Z, called the secondary Brown-Kervaire quadratic forms, so that phi(M)(x + y) = phi(M)(x) + phi(M)(y) + j(x boolean OR Sq(2)y) [M], the Witt class of phi(M) is a homotopy invariant, if the Wu classes v(n+2-2i) (v(M)) = 0 for all integer i. where j : Z(2) --> Q/Z is the inclusion homomorphism and v(M) the stable normal bundle of M. As an application of our invariants we obtain a complete classification of (n - 2)-connected 2n-dimensional pi-manifolds (i.e. stable parallelizable manifolds) up to homeomorphism and homotopy equivalence when n greater than or equal to 4 and n + 2 not equal 2(i) for any integer i. In particular, it shows that homotopy equivalent (n - 2)-connected 2n-dimensional pi-manifolds are homeomorphic when n greater than or equal to 4 and n + 2 not equal 2(i) for any integer i.
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000220656400001
出版者	WALTER DE GRUYTER & CO
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/936
专题	中国科学院数学与系统科学研究院
通讯作者	Fang, FQ
作者单位	1.Nankai Univ, Nankai Inst Math, Tianjin 300071, Peoples R China 2.Univ Fed Fluminense, Inst Matemat, BR-24005 Niteroi, RJ, Brazil 3.Acad Sinica, Inst Math, Beijing 100080, Peoples R China 4.Korea Univ, Dept Math Educ, Seoul 136701, South Korea
推荐引用方式 GB/T 7714	Fang, FQ,Pan, JZ. Secondary Brown-Kervaire quadratic forms and pi-manifolds[J]. FORUM MATHEMATICUM,2004,16(4):459-481.
APA	Fang, FQ,&Pan, JZ.(2004).Secondary Brown-Kervaire quadratic forms and pi-manifolds.FORUM MATHEMATICUM,16(4),459-481.
MLA	Fang, FQ,et al."Secondary Brown-Kervaire quadratic forms and pi-manifolds".FORUM MATHEMATICUM 16.4(2004):459-481.