实投影空间上向量丛的截面

所谓广义向量场问题就是要求向量丛mξ_n上的线性无关截面的最大个数span(mξ_n)=m-n+j(m,n),这里ξ_n为n维实投影空间P_n上的Hopf线丛。关于这一问题的综述参见文献[1]。本文将利用Koschorke的奇点方法证明下面的定理:     

J-同态以及Rohlin定理的推广

一、引言 本文约定所有流形均为紧致连通的微分流形,所有拓扑空间均道路连通,Rohlin的一个定理断言若w_1(M)=w_2(M)=0,则4-流形M的第一个Pontrjagin类模48为零。这一结论由Milnor和Kervaire推广到了高维的情形。     

高阶浸入的存在性

一、引言 本文中所有流形均假定为光滑闭流形。关于高阶切丛及p阶浸入(p-浸入)的定义及基本性质,参见文献[1-3]。设M为n-流形,我们以T~pM记M的p阶切丛,以     

广义J-同态

一、引言 设φ∈(X),其中X为紧致拓扑空间。以Ω_n(X,φ)记X的φ为系数的第n个法协边群。假设X为道路连通,则由自然同态I(φ):π_3~s≌Ω_3(*,0)→Ω_3(X,φ)及经典的稳定     

ON CLASSIFICATION OF HIGHER ORDER IMMERSIONS OF MANIFOLDS

Denote by V_f~p the set of homotopy classes of codimensiom m framings of the p thorder stable normal bundle of a map f:M~n→N~(v(n,p)+m).Where 3≤m=n-1 or m=n-2 butn=0,1 mod 4.We determine in this paper the set V_f~p and then the set of p-homotopyclasses of p-immersions homotopic to f for some special cases.     

CODIMENSION 1 AND 2 IMMERSIONS OF DOLD MANIFOLDS IN COMPLEX PROJECTIVE SPACES

In this paper the following problem has been completely solved:when is a map f:P(m‘n)→CP~(?) homotopic to an immersion with codimension one or two     

FRAMING BORDISM GROUPS OF FRAMED IMMERSED SUBMANIFOLDS

We prove that the n~(th) framing bordism group of framed immersed submanifoldsin a manifold N,which is denoted by Δ_n(N),is canonically isomorphic to the normalbordism group Ω_n(N,-TN).