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
We prove that the n<sup>th</sup> framing bordism group of framed immersed submanifoldsin a manifold N,which is denoted by Δ<sub>n</sub>（N）,is canonically isomorphic to the normalbordism gro...We prove that the n<sup>th</sup> framing bordism group of framed immersed submanifoldsin a manifold N,which is denoted by Δ<sub>n</sub>（N）,is canonically isomorphic to the normalbordism group Ω<sub>n</sub>（N,-TN）.展开更多
In [1], C. Kosniowshi and R. E. Stong have pointed out that the bordism class of fixed point set can determine nothing about manifold with involution. In this note, we are to consider the case of (M<sup>2n-k<...In [1], C. Kosniowshi and R. E. Stong have pointed out that the bordism class of fixed point set can determine nothing about manifold with involution. In this note, we are to consider the case of (M<sup>2n-k</sup>, T)（k=1, 2, 3, 4）whose fixed point set is constant codimension. The major result is:展开更多
The purpose of this paper is to simplify the computations of the nor-mal bordism groups Ω<sub>i</sub>（W<sub>f</sub>,M×P<sup>∞</sup>;（?））and Ω<sub>i</sub>（C&...The purpose of this paper is to simplify the computations of the nor-mal bordism groups Ω<sub>i</sub>（W<sub>f</sub>,M×P<sup>∞</sup>;（?））and Ω<sub>i</sub>（C<sub>f</sub>,（?）w;θ<sub>f</sub>）which Salomonsenand Dax introduced respectively to study the existence and isotopy classificationof differential embeddings of manifolds in manifolds in the metastable range.Asimpler space pair（K<sub>f</sub>,M×P<sup>∞</sup>）is constructed to replace（W<sub>f</sub>,M×P<sup>∞</sup>）.It isshown that（K<sub>f</sub>,M×P<sup>∞</sup>）is homotopy equivalent to（W<sub>f</sub>,M×P<sup>∞</sup>）and homotopy（n-1）-equivalent to（C<sub>f</sub>,（?）W）.To demonstrate the efficacy of this simplification,the isotopy groups [M<sup>n</sup>（?）RP<sup>n+k</sup>],if n（?）2k-4 and M<sup>n</sup> is a closed（n-k+2）-connected manifold,and[M<sup>n</sup>（?）L（p;q<sub>1</sub>…,q<sub>m</sub>）],if 3n（?）4m-2,M<sup>n</sup> is a closed（2n-2m+1）-connected manifold and L is a （2m+1）-dimensional lens space,arespecifically computed.展开更多
In this paper we investigate in detail the Koschorke normal bordism sequence which is very important in application, give a general method by which one may determine the group structures of Ω_1(X, ω) and Ω_2(X, φ)...In this paper we investigate in detail the Koschorke normal bordism sequence which is very important in application, give a general method by which one may determine the group structures of Ω_1(X, ω) and Ω_2(X, φ) appearing in the sequence and compute Ω_i(X×BO(2), φ×Γ), i=1, 2.展开更多
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
Let （M, T） be a closed manifold with an involution T. The fixed point set of T is F. In this article, bordism classes of the involutions with fixed point set F = ^mUi=1 CPi（1）×HPi（n） are determined, where C...Let （M, T） be a closed manifold with an involution T. The fixed point set of T is F. In this article, bordism classes of the involutions with fixed point set F = ^mUi=1 CPi（1）×HPi（n） are determined, where CP（1） and HP（n） denote the 1-dimensional i=1 complex projective space and n-dimensional quaternionic projective space respectively, and n=2^p-2or n=2^p-1（p〉 1）.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.
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.
文摘We prove that the n<sup>th</sup> framing bordism group of framed immersed submanifoldsin a manifold N,which is denoted by Δ<sub>n</sub>（N）,is canonically isomorphic to the normalbordism group Ω<sub>n</sub>（N,-TN）.
文摘In [1], C. Kosniowshi and R. E. Stong have pointed out that the bordism class of fixed point set can determine nothing about manifold with involution. In this note, we are to consider the case of (M<sup>2n-k</sup>, T)（k=1, 2, 3, 4）whose fixed point set is constant codimension. The major result is:
文摘The purpose of this paper is to simplify the computations of the nor-mal bordism groups Ω<sub>i</sub>（W<sub>f</sub>,M×P<sup>∞</sup>;（?））and Ω<sub>i</sub>（C<sub>f</sub>,（?）w;θ<sub>f</sub>）which Salomonsenand Dax introduced respectively to study the existence and isotopy classificationof differential embeddings of manifolds in manifolds in the metastable range.Asimpler space pair（K<sub>f</sub>,M×P<sup>∞</sup>）is constructed to replace（W<sub>f</sub>,M×P<sup>∞</sup>）.It isshown that（K<sub>f</sub>,M×P<sup>∞</sup>）is homotopy equivalent to（W<sub>f</sub>,M×P<sup>∞</sup>）and homotopy（n-1）-equivalent to（C<sub>f</sub>,（?）W）.To demonstrate the efficacy of this simplification,the isotopy groups [M<sup>n</sup>（?）RP<sup>n+k</sup>],if n（?）2k-4 and M<sup>n</sup> is a closed（n-k+2）-connected manifold,and[M<sup>n</sup>（?）L（p;q<sub>1</sub>…,q<sub>m</sub>）],if 3n（?）4m-2,M<sup>n</sup> is a closed（2n-2m+1）-connected manifold and L is a （2m+1）-dimensional lens space,arespecifically computed.
基金This work was supported partially by the Hong Kong Qiu-Shi Foundation, the Outstanding Youth Foundation of China and the Education Foundation of Tsinghua University, as well as the Grants-in-Aid for Science Research of Japanese Ministry of Education.
文摘By using the bordism group, this paper provides an alternative proof of Weiping Zhang's theorem on counting Kervaire semi-characteristic.
文摘In this paper we investigate in detail the Koschorke normal bordism sequence which is very important in application, give a general method by which one may determine the group structures of Ω_1(X, ω) and Ω_2(X, φ) appearing in the sequence and compute Ω_i(X×BO(2), φ×Γ), i=1, 2.
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.
基金supported by NSFC (1097105011001073+3 种基金10901045)HNSFC(A2010000828)FHUST (XL201043QD201021)
文摘Let （M, T） be a closed manifold with an involution T. The fixed point set of T is F. In this article, bordism classes of the involutions with fixed point set F = ^mUi=1 CPi（1）×HPi（n） are determined, where CP（1） and HP（n） denote the 1-dimensional i=1 complex projective space and n-dimensional quaternionic projective space respectively, and n=2^p-2or n=2^p-1（p〉 1）.
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.
