Let $X$ be a 2-connected $p$-local finite $H$-space with a single cell in dimension three. We give a simple cohomological criterion which distinguishes when the inclusion $i$: $S^3 →X$ has the property that the loop of its three-connected cover is null homotopic. In particular, such a null homotopy implies that $π_m(i)=0 for m ≥4$. Applications are made to Harper’s rank 2 finite $H$-space and simple, simply-connected, compact Lie groups.
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机译：假设$ X $是2维连接的$ p $-局部有限$ H $-空间，其中第三个维度为单个像元。我们给出了一个简单的同调性判据，该判据可以区分包含项$ i $：$ S ^ 3→X $何时具有其三连通封面的循环为空同质的性质。特别地，这样的无效同伦意味着对于m≥4$，$π_m（i）= 0。应用程序针对Harper的等级2有限的$ H $空间和简单，简单连接的紧凑型Lie组。
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