From the 1 of 8 linked papers with an AI index.
8 papers
Components in characteristic and Quillen's conjecture
Kevin Ivan Piterman
The paper proves that if a finite group contains a component that is a simple Lie-type group in characteristic p and has no nontrivial normal p‑subgroup, then the Quillen poset at…
An analogue of Rognes' connectivity conjecture for free groups
Benjamin Brück, Jeremy Miller, Kevin Ivan Piterman
We show that the common basis complex of a free group of rank has the homotopy type of a wedge of spheres of dimension . This establishes an -analogue…
Posets of decompositions in spherical buildings
Kevin Ivan Piterman, John Shareshian, Volkmar Welker
We propose definitions of the common bases complex, the poset of decompositions, and the poset of partial decompositions for arbitrary spherical buildings. We show that the poset o…
Connectivity of partial basis complexes of freely decomposable groups
Benjamin Brück, Kevin Ivan Piterman
We show that the complex of partial bases of the free group of rank , where vertices are seen up to conjugation, is Cohen--Macaulay of dimension . This positively answers a…
Group actions on contractible -complexes II
Kevin Ivan Piterman, Iván Sadofschi Costa
In this second part we prove that, if is one of the groups with and or , then the fundamental group of eve…
Notes on the topology of independence structures
Kevin Ivan Piterman, Volkmar Welker
Following Welsh, a pre-independence space (pi-space) is a set together with a non-empty collection of subsets of , called independent sets, which is closed under taki…