K. I. Piterman

activity

20162026

most citedSome results on Quillen's Conjecture via equivalent-poset techniques

2 citations · 7 across the 15 of their papers we have counts for

collaborators

19 papers

math.AT2026

Components in characteristic $p$ and Quillen's conjecture

Kevin Ivan Piterman

The purpose of this paper is to show that, under mild inductive assumptions, if a group $G$ contains a component that is a simple group of Lie type in characteristic $p$ and $O_p(G…

math.AT2025

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 $n$ has the homotopy type of a wedge of spheres of dimension $2 n - 3$ . This establishes an $Aut (F_{n})$ -analogue…

math.AT2025

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…

math.CO2025

Notes on the topology of independence structures

Kevin Ivan Piterman, Volkmar Welker

Following Welsh, a pre-independence space (pi-space) is a set $M$ together with a non-empty collection $I (M)$ of subsets of $M$ , called independent sets, which is closed under taki…

math.GR2025

On reducible Killing forms for groups of Lie type

Kevin Ivan Piterman, Charlotte Roelants

Killing forms on finite groups arise as examples of braided Killing forms on braided Lie algebras. For a finite group $G$ and a $G$ -stable subset $C$ , the Killing form as…

math.GT2024

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 $n$ , where vertices are seen up to conjugation, is Cohen--Macaulay of dimension $n - 1$ . This positively answers a…

math.GR2024

Spherical $p$ -group complexes arising from finite groups of Lie type

Kevin Iván Piterman

We show that the $p$ -group complex of a finite group $G$ is homotopy equivalent to a wedge of spheres of dimension at most $n$ if $G$ contains a self-centralising normal subgroup $…

math.CO2024★ 1 cited

The common basis complex and the partial decomposition poset

Benjamin Brück, Kevin I. Piterman, Volkmar Welker

For a finite-dimensional vector space $V$ , the common basis complex of $V$ is the simplicial complex whose vertices are the proper non-zero subspaces of $V$ , and $σ$ is a simplex i…

math.CO2024★ 1 cited

Posets arising from decompositions of objects in a monoidal category

Kevin Ivan Piterman, Volkmar Welker

Given a symmetric monoidal category $C$ with product $⊔$ , where the neutral element for the product is an initial object, we consider the poset of $⊔$ -complemented subobj…

math.CO2023

On the frame complex of symplectic spaces

Kevin Ivan Piterman

For a symplectic space $V$ of dimension $2 n$ over $F_{q}$ , we compute the eigenvalues of its orthogonality graph. This is the simple graph with vertices the $2$ -dimensiona…

math.GR2023★ 1 cited

Maximal subgroups of exceptional groups and Quillen's dimension

Kevin Ivan Piterman

Given a finite group $G$ and a prime $p$ , let $A_{p} (G)$ be the poset of nontrivial elementary abelian $p$ -subgroups of $G$ . The group $G$ satisfies the Quillen dimension p…

math.GR2022★ 2 cited

Some results on Quillen's Conjecture via equivalent-poset techniques

Kevin I. Piterman, Stephen D. Smith

We extend the Main Theorem of Aschbacher and Smith on Quillen's Conjecture from $p > 5$ to the remaining odd primes $p = 3, 5$ . In the process, we develop further combinatorial and ho…

math.AT2021★ 1 cited

Group actions on contractible $2$ -complexes II

Kevin Ivan Piterman, Iván Sadofschi Costa

In this second part we prove that, if $G$ is one of the groups $PSL_{2} (q)$ with $q > 5$ and $q \equiv 5 (mod 24)$ or $q \equiv 13 (mod 24)$ , then the fundamental group of eve…

math.GR2020

Eliminating components in Quillen's Conjecture

Kevin I. Piterman, Stephen D. Smith

We generalize an earlier result of Segev, which shows that {\em some\/} component in a minimal counterexample to Quillen's conjecture must admit an outer automorphism. We show in f…

math.GR2020★ 1 cited

An approach to Quillen's conjecture via centralizers of simple groups

Kevin Ivan Piterman

We show that, for any given subgroup $H$ of a finite group $G$ , the Quillen poset $A_{p} (G)$ of nontrivial elementary abelian $p$ -subgroups, is obtained from $\mathcal{A}_p…

math.AT2019

Acyclic $2$ -dimensional complexes and Quillen's conjecture

Kevin I. Piterman, Iván Sadofschi Costa, Antonio Viruel

Let $G$ be a finite group and $A_{p} (G)$ be the poset of nontrivial elementary abelian $p$ -subgroups of $G$ . Quillen conjectured that $O_{p} (G)$ is nontrivial if $\mathcal{A}…

math.GR2019

The fundamental group of the $p$ -subgroup complex

Elias Gabriel Minian, Kevin Ivan Piterman

We study the fundamental group of the $p$ -subgroup complex of a finite group $G$ . We show first that $π_{1} (A_{3} (A_{10}))$ is not a free group (here $A_{10}$ is the alternating group…

math.GR2018

A stronger reformulation of Webb's conjecture in terms of finite topological spaces

Kevin Ivan Piterman

We investigate a stronger formulation of Webb's conjecture on the contractibilty of the orbit space of the p-subgroup complexes in terms of finite topological spaces. The original…

math.GR2016

The homotopy types of the posets of p-subgroups of a finite group

Elias Gabriel Minian, Kevin Ivan Piterman

We study the homotopy properties of the posets of p-subgroups Sp(G) and Ap(G) of a finite group G, viewed as finite topological spaces. We answer a question raised by R.E. Stong in…

Components in characteristic p and Quillen's conjecture

An analogue of Rognes' connectivity conjecture for free groups

Posets of decompositions in spherical buildings

Notes on the topology of independence structures

On reducible Killing forms for groups of Lie type

Connectivity of partial basis complexes of freely decomposable groups

Spherical p-group complexes arising from finite groups of Lie type

The common basis complex and the partial decomposition poset

Posets arising from decompositions of objects in a monoidal category

On the frame complex of symplectic spaces

Maximal subgroups of exceptional groups and Quillen's dimension

Some results on Quillen's Conjecture via equivalent-poset techniques

Group actions on contractible 2-complexes II

Eliminating components in Quillen's Conjecture

An approach to Quillen's conjecture via centralizers of simple groups

Acyclic 2-dimensional complexes and Quillen's conjecture

The fundamental group of the p-subgroup complex

A stronger reformulation of Webb's conjecture in terms of finite topological spaces

The homotopy types of the posets of p-subgroups of a finite group

Components in characteristic $p$ and Quillen's conjecture

Spherical $p$ -group complexes arising from finite groups of Lie type

Group actions on contractible $2$ -complexes II

Acyclic $2$ -dimensional complexes and Quillen's conjecture

The fundamental group of the $p$ -subgroup complex