论文标题
稳定的球体组有多大？
How Big are the Stable Homotopy Groups of Spheres?
论文作者
论文摘要
在本文中，我们表明，稳定茎的$ p $ torsion指数在$ n $中增长，而$ n $的$ p $ rank $ e_2 $ page的$ e_2 $ - adams频谱序列的$ \ exp（$ \ exp（θ（\ log log log（n）^3））$增长。这些边界共同提供了第一个亚指数结合在稳定茎的大小上。相反，我们证明望远镜猜想的故障的某个特定，精确的版本意味着Adams $ e_2 $ page提供的上限本质上是尖锐的 - 回答了名义上的问题：与望远镜猜想的命运一样大。 在与安德鲁·森格（Andrew Senger）的附录联合中，我们考虑了这个问题的不稳定类似物。从稳定边界进行的引导我们证明，$ p $ - 局部同型球体的大小像$ \ exp（o（\ log（n）^3））$一样生长，提供了对不稳定词干的大小的第一个亚exppertient绑定。
In this article we show that the $p$-torsion exponent of the stable stems grows sublinearly in $n$ and the $p$-rank of the $E_2$-page of the Adams spectral sequence grows as $\exp(Θ( \log(n)^3))$. Together these bounds provide the first subexponential bound on the size of the stable stems. Conversely, we prove that a certain, precise, version of the failure of the telescope conjecture would imply that the upper bound provided by the Adams $E_2$-page is essentially sharp -- answering the titular question: As big as the fate of the telescope conjecture demands. In an appendix joint with Andrew Senger we consider the unstable analog of this question. Bootstrapping from the stable bounds we prove that the size of the $p$-local homotopy groups of spheres grows like $\exp(O(\log(n)^3))$, providing the first subexponential bound on the size of the unstable stems.
