Co-periodicity isomorphisms between forests of finite p-groups

群上同调中的广义周期性

Generalized Periodicity in Group Cohomology

本文通过引入“编码对”推广有限群的周期上同调理论，并推广Swan定理的上同调条件，该定理涉及周期上同调群在球面上的自由作用。

On p-periodicity in the Farrell cohomology of Sp(p-1,Z[1/n])

We describe isomorphism patterns in the $p$-primary part of the Farrell cohomology ring ${\hat{H}}^*(Sp(p-1,Z[1/n]),Z)$ for any odd prime $p$ and suitable integers $0\neq n\in Z$, where $Sp(p-1,Z[1/n])$ denotes the group of symplectic $(p-1)\times (p-1)$--matrices. Moreover, we determine the precise $p$-period of this ring.

森林-绞线群 II：从齐次呈现的幺半群构造

Forest-skein groups II: construction from homogeneously presented monoids

本文研究由齐次幺半群呈现构造的一维森林-绞线群，通过圈积分解实现同构分类，并证明 Haagerup 性质、同调与拓扑有限性及可序性等性质可从幺半群分数群传递到这些群。

Modeling rooted in-trees by finite p-groups

The aim of this chapter is to provide an adequate graph theoretic framework for the description of periodic bifurcations which have recently been discovered in descendant trees of finite p-groups. The graph theoretic concepts of rooted in-trees with weighted vertices and edges perfectly admit an abstract formulation of the group theoretic notions of successive extensions, nuclear rank, multifurcation, and step size. Since all graphs in this chapter are infinite and dense, we use methods of pattern recognition and independent component analysis to reduce the complex structure to periodically re…

On the group of spheromorphisms of the homogeneous non-locally finite tree

Consider a tree $\mathbb T$, all whose vertices have countable valence; its boundary is the Baire space $\mathbb{B} \simeq\mathbb{N}^{\mathbb N}$; continued fractions expansions identify the set of irrational numbers $\mathbb{R}\setminus \mathbb{Q}$ with $\mathbb B$. Removing $k$ edges from $\mathbb T$ we get a forest consisting of copies of $\mathbb T$. A spheromorphism (or hierarchomorphism) of $\mathbb T$ is an isomorphisms of two such subforests considered as a transformation of $\mathbb T$ or of $\mathbb B$. Denote the group of all spheromorphisms by $\mathrm{Hier}({\mathbb T})$. We a sho…