Coassembly and the $K$-theory of finite groups

Ranks of $RO(G)$-graded stable homotopy groups of spheres for finite groups $G$

We describe the distribution of infinite groups in the $RO(G)$-graded stable homotopy groups of spheres for a finite group $G$.

有限群作为有限空间的同伦自等价

Finite groups as homotopy self-equivalences of finite spaces

本文研究有限群作为有限空间同伦自等价类群的实现问题，利用无穷族两两非弱同伦的反对称空间，构造出同伦自等价类群同构于给定有限群$G$的有限空间。

Homotopy groups as centers of finitely presented groups

For every finite abelian group $A$ and $n\geq 3$, we construct a finitely presented group defined by explicit generators and relations, such that its center is $π_n(ΣK(A,1))$.

The twisted Drinfeld double of a finite group via gerbes and finite groupoids

The twisted Drinfeld double (or quasi-quantum double) of a finite group with a 3-cocycle is identified with a certain twisted groupoid algebra. The groupoid is the loop (or inertia) groupoid of the original group and the twisting is shown geometrically to be the loop transgression of the 3-cocycle. The twisted representation theory of finite groupoids is developed and used to derive properties of the Drinfeld double, such as representations being classified by their characters. This is all motivated by gerbes and 3-dimensional topological quantum field theory. In particular the representation …

Relation between finite topological spaces and finitely presentable groups

In this paper it is shown how to construct a finite topological space $X$ for a given finitely presentable group $G$ such that $π_1(X)\cong G$. Our construction is not optimal in the sense that the cardinality of the space $X$ might not be the smallest possible. Our main result applies to a large class of interesting groups, including all finite groups.

Extension of p-local finite groups

A p-local finite group consists of a finite p-group S, together with a pair of categories which encode ``conjugacy'' relations among subgroups of S, and which are modelled on the fusion in a Sylow p-subgroup of a finite group. It contains enough information to define a classifying space which has many of the same properties as p-completed classifying spaces of finite groups. In this paper, we study and classify extensions of p-local finite groups, and also compute the fundamental group of the classifying space of a p-local finite group.