球面同伦群大小的界
代数拓扑
2021-01-13 v2
摘要
设 为素数。我们证明，对奇数 ， 的 -挠部分基数至多为 ，从而其秩至多为 。对 ，这些结果对偶数 亦成立。现有文献中最佳界分别为 与 ，均出自 Hans-Werner Henn。因此我们结果的核心在于：对更大的素数，该界增长更慢。作为 Henn 工作的推论，我们对更广泛一类空间的同伦群得到类似结果。
引用
@article{arxiv.2001.11872,
title = {Bounding size of homotopy groups of spheres},
author = {Guy Boyde},
journal= {arXiv preprint arXiv:2001.11872},
year = {2021}
}
备注
5 pages. Two corrections in v2: First, Lemma 3.1 in v1 was wrong, and has been replaced with a different lemma which makes the same point. The error was the sentence beginning 'We will not do so here, but one can show....'. Second, since submitting v1 I discovered the paper of Iriye, which gives a result similar to Theorem 1.1 without proof. The introduction has been updated to acknowledge this