Let （M, T） be a smooth closed manifold with a smooth involution T whose fixed point set is a disjoint union of an even-dimensional real projective space and a Dold manifold. In some cases, the equivariant bordism cl...Let （M, T） be a smooth closed manifold with a smooth involution T whose fixed point set is a disjoint union of an even-dimensional real projective space and a Dold manifold. In some cases, the equivariant bordism classes of （M, T） are determined.展开更多
In this paper,we study all the possible bordism classes for a smooth involution on a smooth closed manifold whose fixed point set is RP(1)∪P(m,n),m>0,n>0.
Supposing the smooth involution of the DOLD manifold P(2,2l)satisfies the following condition:the fiberation π:P(1,2l)×T_×(-1)S~∞→RP(∞)is totally nonhomologous to zero(cf.[1, p373]),this paper determines...Supposing the smooth involution of the DOLD manifold P(2,2l)satisfies the following condition:the fiberation π:P(1,2l)×T_×(-1)S~∞→RP(∞)is totally nonhomologous to zero(cf.[1, p373]),this paper determines the classification of smooth involution on the DOLD manifold P(1,2l) totally.展开更多
Let κ be non-negative integer. The unoriented bordism classes, which can be represented as [RP（ξ^κ）] where ξ^κ is a k-plane bundle, form an ideal of the unoriented bordism ring MO.. A group of generators of thi...Let κ be non-negative integer. The unoriented bordism classes, which can be represented as [RP（ξ^κ）] where ξ^κ is a k-plane bundle, form an ideal of the unoriented bordism ring MO.. A group of generators of this ideal expressed by a base of MO. and a necessary and sufficient condition for a bordism class to belong to this ideal are given.展开更多
Let （M^2m＋4n＋k-2, T） be a smooth closed manifold with a smooth involution T whose fixed point set is RP（2^m） ∪ P（2^m, 2n - 1） （m 〉 3, n 〉 0）. For 2n ≥ 2^m, （M^2m＋4n＋k-2, T） is bordant to （P（2^m, RP...Let （M^2m＋4n＋k-2, T） be a smooth closed manifold with a smooth involution T whose fixed point set is RP（2^m） ∪ P（2^m, 2n - 1） （m 〉 3, n 〉 0）. For 2n ≥ 2^m, （M^2m＋4n＋k-2, T） is bordant to （P（2^m, RP（2n））, To）.展开更多
基金Supported by NSFC(11371118)SRFDP(20121303110004)+1 种基金HNSF(A2011205075)HNUHH(20110403)
文摘Let （M, T） be a smooth closed manifold with a smooth involution T whose fixed point set is a disjoint union of an even-dimensional real projective space and a Dold manifold. In some cases, the equivariant bordism classes of （M, T） are determined.
文摘In this paper,we study all the possible bordism classes for a smooth involution on a smooth closed manifold whose fixed point set is RP(1)∪P(m,n),m>0,n>0.
基金Supported by the Foundation of Tian Yuanthe Natural Science Foundation of Hebei province.
文摘Supposing the smooth involution of the DOLD manifold P(2,2l)satisfies the following condition:the fiberation π:P(1,2l)×T_×(-1)S~∞→RP(∞)is totally nonhomologous to zero(cf.[1, p373]),this paper determines the classification of smooth involution on the DOLD manifold P(1,2l) totally.
基金This work is supported by HNSF(Grant No:103144) NNSF of China(10371029)
文摘Let κ be non-negative integer. The unoriented bordism classes, which can be represented as [RP（ξ^κ）] where ξ^κ is a k-plane bundle, form an ideal of the unoriented bordism ring MO.. A group of generators of this ideal expressed by a base of MO. and a necessary and sufficient condition for a bordism class to belong to this ideal are given.
基金Foundation item： the National Natural Science Foundation of China （No. 10371029） the Natural Science Foundation of Hebei Province （No. 103144）.
文摘Let （M^2m＋4n＋k-2, T） be a smooth closed manifold with a smooth involution T whose fixed point set is RP（2^m） ∪ P（2^m, 2n - 1） （m 〉 3, n 〉 0）. For 2n ≥ 2^m, （M^2m＋4n＋k-2, T） is bordant to （P（2^m, RP（2n））, To）.
