Ⅰ. INTRODUCTIONLet R<sub>n</sub> be an unoriented cobordism group of smooth closed n-dimensional manifolds and R<sub>*</sub>=sum from n R<sub>n</sub> be a cobordism ring. Let [M]&l...Ⅰ. INTRODUCTIONLet R<sub>n</sub> be an unoriented cobordism group of smooth closed n-dimensional manifolds and R<sub>*</sub>=sum from n R<sub>n</sub> be a cobordism ring. Let [M]<sub>2</sub> be the class of the manifold M<sup>n</sup> in R<sub>n</sub>. For a given manifold N<sup>m</sup>, we consider the classes α∈R<sub>n</sub>. Is there a fiber bundle over N<sup>m</sup>展开更多
Let （M<sup>n</sup>, T） be a smooth involution on a smooth closed n-dimensional manifold M<sup>n</sup>. Let F<sup>n-k</sup> be the union of those （n-k）-dimensional components of ...Let （M<sup>n</sup>, T） be a smooth involution on a smooth closed n-dimensional manifold M<sup>n</sup>. Let F<sup>n-k</sup> be the union of those （n-k）-dimensional components of the fixed point set F of T and let v<sup>k</sup> denote the normal bundle of F<sup>n-k</sup> in M<sup>n</sup>. Czes Kosniowski and R. E. Strong have展开更多
Let n≥4 and let M^n be a smooth closed n-manifold. Denote the number of the powersin the binary expression of n by α(n). In this paper, we determine, up to cobordism, allthe possible M^n which immerse themselves in ...Let n≥4 and let M^n be a smooth closed n-manifold. Denote the number of the powersin the binary expression of n by α(n). In this paper, we determine, up to cobordism, allthe possible M^n which immerse themselves in R^(2n-α(n)-1), and prove that the Stiefel-Whitneynumber W_(n-α(n))W_α(n) (M^n)=0 iff M^n is cobordant to a smooth closed n-manifold N^n, whereN^n immerses itself in R^(2n-α(n)-1).展开更多
Given a smooth unfree involution (M^n, T), where M^n is a smooth closed n-manifold, weshall associate (M^n, T) with a number sequence I(T), called the involution number sequenceassociated with (M^n, T). We shall prove...Given a smooth unfree involution (M^n, T), where M^n is a smooth closed n-manifold, weshall associate (M^n, T) with a number sequence I(T), called the involution number sequenceassociated with (M^n, T). We shall prove that I(T)is precisely the strictly increasing arrange-ment of all the possible integers n-k in which F^k is nonempty, F^k being the disjointunion of all the k-dimensional components in the fixed point set F of the involution (M^n,T). For application, we shall give a proof for the well-known fact that the fixed point set ofa smooth unfree involution on S^n must be a constant-dimensional smooth closed submanifoldof S^n.展开更多
Ⅰ. INTRODUCTION Classifying all the possible smooth involutions on a given smooth dosed n-manifold, up to equivariant cobordism, is an interesting problem in the study of manifolds with involutions. But, very few con...Ⅰ. INTRODUCTION Classifying all the possible smooth involutions on a given smooth dosed n-manifold, up to equivariant cobordism, is an interesting problem in the study of manifolds with involutions. But, very few contributions have been seen in this subject except Ref. [1], just because there were hardly any effective methods to solve this problem. With a kind展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘Ⅰ. INTRODUCTIONLet R<sub>n</sub> be an unoriented cobordism group of smooth closed n-dimensional manifolds and R<sub>*</sub>=sum from n R<sub>n</sub> be a cobordism ring. Let [M]<sub>2</sub> be the class of the manifold M<sup>n</sup> in R<sub>n</sub>. For a given manifold N<sup>m</sup>, we consider the classes α∈R<sub>n</sub>. Is there a fiber bundle over N<sup>m</sup>
基金Supported by the National Natural Science Foundation of China
文摘Let （M<sup>n</sup>, T） be a smooth involution on a smooth closed n-dimensional manifold M<sup>n</sup>. Let F<sup>n-k</sup> be the union of those （n-k）-dimensional components of the fixed point set F of T and let v<sup>k</sup> denote the normal bundle of F<sup>n-k</sup> in M<sup>n</sup>. Czes Kosniowski and R. E. Strong have
基金Project supported by the National Natural Science Foundation of China.
文摘Let n≥4 and let M^n be a smooth closed n-manifold. Denote the number of the powersin the binary expression of n by α(n). In this paper, we determine, up to cobordism, allthe possible M^n which immerse themselves in R^(2n-α(n)-1), and prove that the Stiefel-Whitneynumber W_(n-α(n))W_α(n) (M^n)=0 iff M^n is cobordant to a smooth closed n-manifold N^n, whereN^n immerses itself in R^(2n-α(n)-1).
基金Project supported by the National Natural Science Foundation of China.
文摘Given a smooth unfree involution (M^n, T), where M^n is a smooth closed n-manifold, weshall associate (M^n, T) with a number sequence I(T), called the involution number sequenceassociated with (M^n, T). We shall prove that I(T)is precisely the strictly increasing arrange-ment of all the possible integers n-k in which F^k is nonempty, F^k being the disjointunion of all the k-dimensional components in the fixed point set F of the involution (M^n,T). For application, we shall give a proof for the well-known fact that the fixed point set ofa smooth unfree involution on S^n must be a constant-dimensional smooth closed submanifoldof S^n.
基金Project supported by the National Natural Science Foundation of China.
文摘Ⅰ. INTRODUCTION Classifying all the possible smooth involutions on a given smooth dosed n-manifold, up to equivariant cobordism, is an interesting problem in the study of manifolds with involutions. But, very few contributions have been seen in this subject except Ref. [1], just because there were hardly any effective methods to solve this problem. With a kind
