论文标题
球体同拷贝组的边界大小
Bounding size of homotopy groups of spheres
论文作者
论文摘要
令$ p $为PRIME。我们证明，对于$ n $奇数，$ p $ - torsion的部分$π_q（s^{n}）$最多具有$ p^{2^{2^{\ frac {1} {1} {p-1} {q-n+3-2p）}} $，因此最多排名$ 2^{\ frac {1} {p-1}（q-n+3-2p）} $。对于$ p = 2 $，这些结果也适用于$ n $。现有文献中证明的最佳界限分别是$ p^{q-n+1}} $和$ 2^{q-n+1} $，这既归功于Hans-Werner Henn。因此，我们结果的要点是，对于较大的素数，界限的增长较慢。作为Henn的工作的必然性，我们为更广泛的空间的同型组获得了类似的结果。
Let $p$ be prime. We prove that, for $n$ odd, the $p$-torsion part of $π_q(S^{n})$ has cardinality at most $p^{2^{\frac{1}{p-1}(q-n+3-2p)}}$, and hence has rank at most $2^{\frac{1}{p-1}(q-n+3-2p)}$. For $p=2$ these results also hold for $n$ even. The best bounds proven in the existing literature are $p^{2^{q-n+1}}$ and $2^{q-n+1}$ respectively, both due to Hans-Werner Henn. The main point of our result is therefore that the bound grows more slowly for larger primes. As a corollary of work of Henn, we obtain a similar result for the homotopy groups of a broader class of spaces.
