Bernardo Villarreal

activity

20182021

collaborators

6 papers

math.AT2025

Counting conjugacy classes of elements of finite order in p-compact groups

José Cantarero, Bernardo Villarreal

We express the set of representations from a cyclic $p$ -group to a connected $p$ -compact group in terms of the associated reflection group and compute its cardinality for each exot…

math.AT2021

On the second homotopy group of the classifying space for commutativity in Lie groups

Bernardo Villarreal

In this note we show that the second homotopy group of $B (2, G)$ , the classifying space for commutativity for a compact Lie group $G$ , contains a direct summand isomorphic to $π_1(G…

math.GR2021

On families of nilpotent subgroups and associated coset posets

Simon Gritschacher, Bernardo Villarreal

We study some properties of the coset poset associated with the family of subgroups of class $\leq 2$ of a nilpotent group of class $\leq 3$ . We prove that under certain assumption…

math.AT2019

The Complex of Affinely Commutative Sets

Omar Antolín-Camarena, Bernardo Villarreal

We show that for some classes of groups $G$ , the homotopy fiber $E_{com} G$ of the inclusion of the classifying space for commutativity $E_{com} G$ into the class…

math.AT2018

Commutative cocycles and stable bundles over surfaces

Daniel A. Ramras, Bernardo Villarreal

Commutative K-theory, a cohomology theory built from spaces of commuting matrices, has been explored in recent work of Adem, Gómez, Gritschacher, Lind, and Tillman. In this article…

math.AT2018

Classifying spaces for commutativity of low-dimensional Lie groups

Omar Antolín-Camarena, Simon Gritschacher, Bernardo Villarreal

For each of the groups $G = O (2), S U (2), U (2)$ , we compute the integral and $F_{2}$ -cohomology rings of $B_{com} G$ (the classifying space for commutativity of $G$ ), th…