Special generators of the unoriented cobordism ring MO* are constructed to determine the groups J<sub>n,k</sub><sup>τ</sup> of n-dimensional cobordism classes in MO<sub>n</sub> con...Special generators of the unoriented cobordism ring MO* are constructed to determine the groups J<sub>n,k</sub><sup>τ</sup> of n-dimensional cobordism classes in MO<sub>n</sub> containing a representative M<sup>n</sup> admitting a （Z<sub>2</sub>）<sup>k</sup> -action with fixed point set of constant codimension.展开更多
Let J_(*,k)~r 2. denote the ideal in MO_* of cobordism classes containing arepresentative that admits (Z_2)~k-actions with a fixed point set of constant codimension r. Inthis paper we determine J_(*,k)^(2^k+2) and J_(...Let J_(*,k)~r 2. denote the ideal in MO_* of cobordism classes containing arepresentative that admits (Z_2)~k-actions with a fixed point set of constant codimension r. Inthis paper we determine J_(*,k)^(2^k+2) and J_(*,3)^(2^3+1).展开更多
The aim of this article is to present the contribution of Wu Wen-Tsün to Algebraic Topology and more precisely to the theory of characteristic classes. Several papers provide complete and welldocumented biography...The aim of this article is to present the contribution of Wu Wen-Tsün to Algebraic Topology and more precisely to the theory of characteristic classes. Several papers provide complete and welldocumented biography and academic career of Wu Wen-Tsün, in particular, Hudecek, 2014; O'Connor and Robertson, 2006; Wen-Tsün Wu's Academic Career, 2006; Selected works of Wen-Tsun Wu, 2008.The author does not repeat the details provided in these papers concerning the Wu Wen-Tsün's bibliography, we will just mention people involved in the Wu Wen-Tsün's period in France.In addition to Wu Wen-Tsün's papers, the Dieudonné's book(Dieudonné, 1960) provides an excellent presentation of main results of Wu Wen-Tsün in Algebraic and Differential Topology. The author will use and abuse of this book(and refer to) when suitable.In the introduction, the author recalls mainly historical facts concerning the contribution of Wu Wen-Tsün to Algebraic Topology. The second section shows speci?cally the contribution of Wu WenTsün to the Stiefel-Whitney classes and introduces the third section, dealing with the(real) Wu classes.The author provides de?nition, properties as well as further developments and generalizations of the Wu classes. The fourth and ?fth sections are devoted to recent applications: In Cobordism theory and in Mathematical Physics. The author notices that Wu classes have been used as well in other domains,in particular surgery theory(Madsen and Milgram, 1979). The last section concerns the complex Wu classes and shows that the more recent Mather classes coincide with the previously de?ned complex Wu classes, that is a result from Zhou(1994)(see also Liu, 1996).This article is devoted to the contribution of Wu Wen-Tsün to the theory of Characteristic Classes,which coincides with his "French period"(1947–1951). However, speaking of Algebraic Topology, it is worthwhile to mention the important contribution of Wu Wen-Tsün to the Theory of realization of complexes or manifolds in Euclidean spaces and of embedding cla展开更多
Let RP（k） denote the k-dimensional real projective space. This article determines which cobordism classes are represented by the total space of a fibering with prescribed base space RP（3）× RP（1）, RP（2） &#...Let RP（k） denote the k-dimensional real projective space. This article determines which cobordism classes are represented by the total space of a fibering with prescribed base space RP（3）× RP（1）, RP（2） × RP（1）, RP（2）× RP（1）× RP（1） or RP（3）× RP（2）.展开更多
文摘Special generators of the unoriented cobordism ring MO* are constructed to determine the groups J<sub>n,k</sub><sup>τ</sup> of n-dimensional cobordism classes in MO<sub>n</sub> containing a representative M<sup>n</sup> admitting a （Z<sub>2</sub>）<sup>k</sup> -action with fixed point set of constant codimension.
基金Supported by the National Natural Sciences Foundation of P.R.China(No.10371029)the Natural Sciences Foundation of Hebei Province(No.103144)the Doctoral Foundation of Hebei Normal University(No.103257)
文摘Let J_(*,k)~r 2. denote the ideal in MO_* of cobordism classes containing arepresentative that admits (Z_2)~k-actions with a fixed point set of constant codimension r. Inthis paper we determine J_(*,k)^(2^k+2) and J_(*,3)^(2^3+1).
文摘The aim of this article is to present the contribution of Wu Wen-Tsün to Algebraic Topology and more precisely to the theory of characteristic classes. Several papers provide complete and welldocumented biography and academic career of Wu Wen-Tsün, in particular, Hudecek, 2014; O'Connor and Robertson, 2006; Wen-Tsün Wu's Academic Career, 2006; Selected works of Wen-Tsun Wu, 2008.The author does not repeat the details provided in these papers concerning the Wu Wen-Tsün's bibliography, we will just mention people involved in the Wu Wen-Tsün's period in France.In addition to Wu Wen-Tsün's papers, the Dieudonné's book(Dieudonné, 1960) provides an excellent presentation of main results of Wu Wen-Tsün in Algebraic and Differential Topology. The author will use and abuse of this book(and refer to) when suitable.In the introduction, the author recalls mainly historical facts concerning the contribution of Wu Wen-Tsün to Algebraic Topology. The second section shows speci?cally the contribution of Wu WenTsün to the Stiefel-Whitney classes and introduces the third section, dealing with the(real) Wu classes.The author provides de?nition, properties as well as further developments and generalizations of the Wu classes. The fourth and ?fth sections are devoted to recent applications: In Cobordism theory and in Mathematical Physics. The author notices that Wu classes have been used as well in other domains,in particular surgery theory(Madsen and Milgram, 1979). The last section concerns the complex Wu classes and shows that the more recent Mather classes coincide with the previously de?ned complex Wu classes, that is a result from Zhou(1994)(see also Liu, 1996).This article is devoted to the contribution of Wu Wen-Tsün to the theory of Characteristic Classes,which coincides with his "French period"(1947–1951). However, speaking of Algebraic Topology, it is worthwhile to mention the important contribution of Wu Wen-Tsün to the Theory of realization of complexes or manifolds in Euclidean spaces and of embedding cla
基金Project Supported by NSFC (10371029),HNSF (103144)and SRF for ROCS, SEM
文摘Let RP（k） denote the k-dimensional real projective space. This article determines which cobordism classes are represented by the total space of a fibering with prescribed base space RP（3）× RP（1）, RP（2） × RP（1）, RP（2）× RP（1）× RP（1） or RP（3）× RP（2）.
