Zobrazeno 1 - 10
of 89
pro vyhledávání: '"Villarreal, Bernardo"'
We study the homotopy type of spaces of commuting elements in connected nilpotent Lie groups, via almost commuting elements in their Lie algebras. We give a necessary and sufficient condition on the fundamental group of such a Lie group $G$ to ensure
Externí odkaz:
http://arxiv.org/abs/2405.09652
In this short note we show that the path-connected component of the identity of the derived subgroup of a compact Lie group consists just of commutators. We also discuss an application of our main result to the homotopy type of the classifying space
Externí odkaz:
http://arxiv.org/abs/2309.02344
Autor:
Villarreal, Bernardo
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 $\pi_1(G)\oplus\pi_1([G,G])$, where $[G,G]$ is the commutator subgroup of $G
Externí odkaz:
http://arxiv.org/abs/2110.13109
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 assumptions on the group the coset poset is simply-connected if and only if the
Externí odkaz:
http://arxiv.org/abs/2104.06869
Publikováno v:
Transform. Groups (2021)
To a compact Lie group $G$ one can associate a space $E(2,G)$ akin to the poset of cosets of abelian subgroups of a discrete group. The space $E(2,G)$ was introduced by Adem, F. Cohen and Torres-Giese, and subsequently studied by Adem and G\'omez, an
Externí odkaz:
http://arxiv.org/abs/2009.12257
We show that for some classes of groups $G$, the homotopy fiber $E_{\mathrm{com}} G$ of the inclusion of the classifying space for commutativity $E_{\mathrm{com}} G$ into the classifying space $BG$, is contractible if and only if $G$ is abelian. We s
Externí odkaz:
http://arxiv.org/abs/1906.07205
Commutative K-theory, a cohomology theory built from spaces of commuting matrices, has been explored in recent work of Adem, G\'{o}mez, Gritschacher, Lind, and Tillman. In this article, we use unstable methods to construct explicit representatives fo
Externí odkaz:
http://arxiv.org/abs/1807.03736
For each of the groups $G = O(2), SU(2), U(2)$, we compute the integral and $\mathbb{F}_2$-cohomology rings of $B_\text{com} G$ (the classifying space for commutativity of $G$), the action of the Steenrod algebra on the mod 2 cohomology, the homotopy
Externí odkaz:
http://arxiv.org/abs/1802.03632
Publikováno v:
Proc. Edinburgh Math. Soc. 2020
We describe the connected components of the space $\text{Hom}(\Gamma,SU(2))$ of homomorphisms for a discrete nilpotent group $\Gamma$. The connected components arising from homomorphisms with non-abelian image turn out to be homeomorphic to $\mathbb{
Externí odkaz:
http://arxiv.org/abs/1611.05937
Autor:
Villarreal, Bernardo
Publikováno v:
Algebr. Geom. Topol. 17 (2017) 3519-3545
Let $G$ be a real linear algebraic group and $L$ a finitely generated cosimplicial group. We prove that the space of homomorphisms $Hom(L_n,G)$ has a homotopy stable decomposition for each $n\geq 1$. When $G$ is a compact Lie group, we show that the
Externí odkaz:
http://arxiv.org/abs/1601.04688