All p-local finite groups of rank two for odd prime p

J-Groups of Lens Spaces modulo Odd Prime Powers

We describe the J-Groups of lens spaces modulo odd prime powers via relations and rational representations.

The derived category of complex periodic K-theory localized at an odd prime

We prove that for an odd prime $p$, the derived category $\mathcal{D}(KU_{(p)})$ of the $p$-local complex periodic $K$-theory spectrum $KU_{(p)}$ is triangulated equivalent to the derived category of its homotopy ring $π_*KU_{(p)}$. This implies that if $p$ is an odd prime, the triangulated category $\mathcal{D}(KU_{(p)})$ is algebraic.

奇素数处高阶Adams微分与高阶代数Novikov微分之间的对应

A correspondence between higher Adams differentials and higher algebraic Novikov differentials at odd primes

本文基于“τ的余纤维哲学”，证明了在奇素数处经典Adams谱序列的高阶微分在特定范围内与相应的高阶代数Novikov微分相一致。

The Brown-Peterson spectrum is not $\mathbb{E}_{2(p^2+2)}$ at odd primes

We show that the odd-primary Brown-Peterson spectrum $\mathrm{BP}$ does not admit the structure of an $\mathbb{E}_{2(p^2+2)}$ ring spectrum and that there can be no map $\mathrm{MU} \to \mathrm{BP}$ of $\mathbb{E}_{2p+3}$ ring spectra. We also prove the same results for truncated Brown-Peterson spectra $\mathrm{BP} \langle n \rangle$ of height $n \geq 4$. This extends results of Lawson at the prime $2$.

A Note on the Algebra of Operations for Hopf Cohomology at Odd Primes

Let $p$ be any prime, and let ${\mathcal B}(p)$ be the algebra of operations on the cohomology ring of any cocommutative $\mathbb{F}_p$-Hopf algebra. In this paper we show that when $p$ is odd (and unlike the $p=2$ case), ${\mathcal B}(p)$ cannot become an object in the Singer category of $\mathbb{F}_p$-algebras with coproducts, if we require that coproducts act on the generators of ${\mathcal B}(p)$ coherently with their nature of cohomology operations

奇数素数处的等变 K(1)-局部球面

The equivaraint K(1)-local sphere at odd prime

本文计算了奇数素数处等变 K(1)-局部球面的 RO 分次同伦 Mackey 函子。

Periodic self maps and thick ideals in the stable motivic homotopy category over $\mathbb{C}$ at odd primes

In this article we study thick ideals defined by periodic self maps in the stable motivic homotopy category over $\mathbb{C}$. In addition, we extend some results of Ruth Joachimi about the relation between thick ideals defined by motivic Morava K-theories and the preimages of the thick ideals in the stable homotopy category under Betti realization.

奇素数p的ℤ/p-等变对偶斯廷罗德代数

The $\mathbb{Z}/p$-equivariant dual Steenrod algebra for an odd prime $p$

该研究完全计算了常Mackey函子ℤ/p的RO(ℤ/p)-分次系数Hℤ/p_⋆Hℤ/p，属于代数拓扑领域的相关计算。

奇素数下Demushkin群的$A_3$-形式性

$A_3$-formality for Demushkin groups at odd primes

该研究针对奇素数下的Demushkin群，探讨微分分次代数的$A_3$-形式性，通过计算Hochschild上同调中的Benson-Krause-Schwede典范类，证明q不变量是否为3决定了其连续上链代数是否满足$A_3$-形式性。

奇数素数下 $\mathbb{F}_p$ 的迭代拓扑 Hochschild 同调

Iterated Topological Hochschild Homology of $\mathbb{F}_p$ at odd primes

本文计算奇数素数下 $\mathbb{F}_p$ 的迭代拓扑 Hochschild 同调的同伦群，通过 bar 谱序列证明其在 $E^2$ 页坍缩，并确定环结构。

The smooth Whitehead spectrum of a point at odd regular primes

Let p be an odd regular prime, and assume that the Lichtenbaum-Quillen conjecture holds for K(Z[1/p]) at p. Then the p-primary homotopy type of the smooth Whitehead spectrum Wh(*) is described. A suspended copy of the cokernel-of-J spectrum splits off, and the torsion homotopy of the remainder equals the torsion homotopy of the fiber of the restricted S^1-transfer map t: SigmaCP^infty--> S. The homotopy groups of Wh(*) are determined in a range of degrees, and the cohomology of Wh(*) is expressed as an A-module in all degrees, up to an extension. These results have geometric topological interp…

Cohomology of the Moduli Space of Rank Two, Odd Degree Vector Bundles over a Real Curve

We consider the moduli space of rank two, odd degree, semi-stable Real vector bundles over a real curve, calculating the singular cohomology ring in odd and zero characteristic for most examples.

Smash products of E(1)-local spectra at an odd prime

In 1996, Franke constructed a purely algebraic category that is equivalent as a triangulated category to the E(n)-local stable homotopy category for n^2+n < 2p-2. The two categories are not Quillen equivalent, and his proof uses systems of triangulated diagram categories rather than model categories. Our main result is that in the case n=1 Franke's functor maps the derived tensor product to the smash product. It can however not be an associative equivalence of monoidal categories. The first part of our paper sets up a monoidal version of Franke's systems of triangulated diagram categories and …