For any given subgroup H of a finite group G, the Quillen poset of nontrivial elementary abelian p-subgroups is obtained from by attaching elements via their centralisers in H. We exploit this idea to study Quillen's ...

We generalize an earlier result of Segev, which shows that some component in a minimal counterexample to Quillen's conjecture must admit an outer automorphism. We show in fact that every component must admit an outer ...

Let G be a finite group and Ap(G) be the poset of nontrivial elementary abelian p-subgroups of G. Quillen conjectured that Op(G) is nontrivial if Ap(G) is contractible. We prove that Op(G) 6= 1 for any group G admitting a ...

In this paper we introduce the Quillen-Suslin rings and investigate its relation with some other classes of rings as Hermite rings (each stably free module is free), PSF rings (each finitely generated projective module is ...

We relate the Davis-Lück homology with coefficients in Weibel's homotopy K-theory to the equivariant algebraic kk-theory using homotopy theory and adjointness theorems. We express the left hand side of the assembly map for ...

We use techniques from both real and complex algebraic geometry to study K-theoretic and related invariants of the algebra C(X) of continuous complex-valued functions on a compact Hausdorff topological space X. For example, ...