On the nonexistence of Smith-Toda complexes

On the existence of the self map v_2^9 on the Smith-Toda complex V(1) at the prime 3

Let V(1) be the Smith-Toda complex at the prime 3. We prove that there exists a map v_2^9: Σ^{144}V(1) \to V(1) that is a K(2) equivalence. This map is used to construct various v_2-periodic infinite families in the 3-primary stable homotopy groups of spheres.

关于第一Smith-Toda谱的同伦群中beta与gamma元素乘积的研究

On products of beta and gamma elements in the homotpy of the first Smith-Toda spectrum

本文确定了奇素数下单色余模$M^1_2$的第一上同调，并利用其证明了Smith-Toda谱$V(1)$同伦群中beta与gamma元素乘积的非平凡性，为计算$M^3_0$的上同调奠定基础。

关于 $L_n$-局部球面同伦的希腊字母元素的一个注记

A note on the Greek letter elements of the homotopy of the $L_n$-local spheres

本文在 $n^2\le 2p-1$ 条件下证明 $L_nS^0$ 的同伦群包含第 $n$ 个希腊字母族，并建立 $v_n^{-1}BP$-局部化 Smith-Toda 谱 $W_n$ 的存在性，还证明了 $(p,n)=(7,4)$ 时 delta 族的存在。

The first line of the Bockstein spectral sequence on a monochromatic spectrum at an odd prime

The chromatic spectral sequence is introduced in \cite{mrw} to compute the $E_2$-term of the \ANSS\ for computing the stable homotopy groups of spheres. The $E_1$-term $E_1^{s,t}(k)$ of the spectral sequence is an Ext group of $BP_*BP$-comodules. There are a sequence of Ext groups $E_1^{s,t}(n-s)$ for non-negative integers $n$ with $E_1^{s,t}(0)=E_1^{s,t}$, and Bockstein spectral sequences computing a module $E_1^{s,*}(n-s)$ from $E_1^{s-1,*}(n-s+1)$. So far, a small number of the $E_1$-terms are determined. Here, we determine the $E_1^{1,1}(n-1)=\e^1M^1_{n-1}$ for $p>2$ and $n>3$ by computing…