新同伦不变数量 Ⅱ.两个短正合序列

<正> 我们在I中考虑了一个短正合列的情况,在那里,通过运算T~((N-n))获得了N维CW丛的T~(N_n)挠率.这些挠率是一类全新的同伦不变数量.做为这种数量的一种应用,I中已用它们来定出某些上同伦群的群结构.现在,我们继续深入,来考虑有两个短正合

ON NEW HOMOTOPY INVARIANTS Ⅱ.TWO SHORT EXACT SEQUENCES

Let K be an N- dimenstonal CW-complex. n = N-2.We haw Steenrod square Sq~2:H~m(K, Z) → H~(m+2)(K, Z_2).Now we consider the groups: Ker Sq~2(H~n(K, Z)), Coker Sq~2=H~(n+1)(K,Z_2)/Sq~2 H~(n-1)(K,Z), and Coker Φ= a factor group of H~(n+2)(K, Z_2). where Φ is the Adem secondary operation.Denote the p-prinary component of group G by G_((p)) and m_G={g|mg=0}.Ker Sq_((2))~2Then ker Sq_((2))~2=2_1~l Ker Sq~2 ker Sq~2. On 2~lk Ker S_q~2, we have cohomology operations T_2~((2))(k): 2~lk Ker Sq~2→Coker Sq~2, k=1,…,r.Each operation T_2~((2))(k) has the property T_2~((2))(k)|2~lt Ker Sq~2 = 0, k