Discrete groups, Grothendieck rings and families of finite subgroups
In this paper we use families of finite subgroups to study Grothendieck rings associated to certain discrete groups, such as the arithmetic ones.
math.GR↗
arXiv subjects
Alejandro Adem
Publications and source records attributed to Alejandro Adem.
The cohomology of the McLaughlin group and some associated groups
In this paper we compute the mod 2 cohomology of the McLaughlin group, which is one of the sporadic simple groups.
math.AT↗
On the cohomology of SL(2,Z[1/p])
In this paper we compute the integral cohomology of the discrete groups SL(2,Z[1/p]), where p is any prime.
math.AT↗
The cohomology rings of rank 3 simple groups are Cohen-Macaulay
In this paper we show that the mod 2 cohomology ring of any finite simple group of rank 3 or less (at the prime 2) must be Cohen-Macaulay.
math.AT↗
Representations and $K$-theory of Discrete Groups
Let $Γ$ be a discrete group of finite virtual cohomological dimension with certain finiteness conditions of the type satisfied by arithmetic groups. We define a representation ring for $Γ$, determined on its elements of finite order, which is of finite type. Then we determine the contribution of this ring to the topological $K$-theory $K^*(BΓ)$, obtaining an exact formula for the difference in terms of the cohomology of the centralizers of elements of finite order in $Γ$.
math.KT↗