Blakers–Massey theorem

《Algebraic Topology》 · 第 133 页 · Theorem 6.4.1

Let \(Y=Y_1\cup Y_2\) with nonempty intersection \(Y_0\), and suppose \(\pi_i(Y_1,Y_0)=0\) for \(0<i<p\) and \(\pi_i(Y_2,Y_0)=0\) for \(0<i<q\). Then the excision map \(\pi_n(Y_2,Y_0)\to\pi_n(Y,Y_1)\) is surjective for \(1\le n\le p+q-2\) and bijective for \(1\le n<p+q-2\).