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Natàlia Castellana

Publications and source records attributed to Natàlia Castellana.

9 recordsLinked to original sources
arXiv2026

A derived Chouinard's theorem for infinite groups

We establish a Chouinard-type theorem for modules over algebras of cochains on the classifying spaces of a broad class of infinite groups, allowing commutative ring spectra as coefficients. We then use this result to study finiteness properties of the integral cohomology rings of certain infinite groups, as well as stratification of the corresponding module categories. In particular, we complete the (co)stratification of module categories associated to homotopical groups over fields of positive characteristic.

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arXiv2026

Cellular approximations of fusion systems

In this paper we study the cellularization of classifying spaces of saturated fusion systems with respect to classifying spaces of finite p-groups. We give explicit algebraic criteria to decide when a classifying space is cellular. Moreover, we describe computations for a given family of exotic examples introduced by Díaz-Ruiz-Viruel.

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arXiv2026

Conservative geometric functors via purity

We establish a criterion for determining when a family of geometric functors is jointly conservative through the lens of purity in compactly generated triangulated categories. We introduce the notion of pure descendability and we apply it to two particular situations involving sequential limits of ring spectra.

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arXiv2021

Normalizers of chains of discrete $p$-toral subgroups in compact Lie groups

In this paper we study the normalizer decomposition of a compact Lie group $G$ using the information of the fusion system $\mathcal{F}$ of $G$ on a maximal discrete $p$-toral subgroup. We prove that there is an injective map from the set of conjugacy classes of chains of $\mathcal{F}$-centric, $\mathcal{F}$-radical discrete $p$-toral subgroups to the set of conjugacy classes of chains of $p$-centric, $p$-stubborn continuous $p$-toral subgroups. The map is a bijection when $π_0(G)$ is a finite $p$-group. We also prove that the classifying space of the normalizer of a chain of discrete $p$-toral subgroups of $G$ is mod $p$ equivalent to the classifying space of the normalizer of the corresponding chain of $p$-toral subgroups.

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arXiv2020

A new approach to mod 2 decompositions of BSU(2) and BSO(3)

Dwyer, Miller and Wilkerson proved that at the prime 2, the classifying spaces of SU(2) and SO(3) can be obtained as a homotopy pushout of the classifying spaces of certain subgroups. In this paper we show explicitly how these decompositions arise from the fusion systems of SU(2) and SO(3) over maximal discrete 2-toral subgroups.

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arXiv2019

Vector bundles over classifying spaces of p-local finite groups and Benson-Carlson duality

In this paper we obtain a description of the Grothendieck group of complex vector bundles over the classifying space of a p-local finite group in terms of representation rings of subgroups of its Sylow. We also prove a stable elements formula for generalized cohomological invariants of p-local finite groups, which is used to show the existence of unitary embeddings of p-local finite groups. Finally, we show that the augmentation map for the cochains of the classifying space of a p-local finite group is Gorenstein in the sense of Dwyer-Greenlees-Iyengar and obtain some consequences about the cohomology ring of these classifying spaces.

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arXiv2015

Unitary embeddings of finite loop spaces

In this paper we construct faithful representations of saturated fusion systems over discrete p-toral groups and use them to find conditions that guarantee the existence of unitary embeddings of p-local compact groups. These conditions hold for the Clark-Ewing and Aguadé-Zabrodsky p-compact groups as well as some exotic 3-local compact groups. We also show the existence of unitary embeddings of finite loop spaces.

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arXiv2012

Homotopy idempotent functors on classifying spaces

Fix a prime $p$. Since their definition in the context of Localization Theory, the homotopy functors $P_{B\Z/p}$ and $CW_{B\Z/p}$ have shown to be powerful tools to understand and describe the mod $p$ structure of a space. In this paper, we study the effect of these functors on a wide class of spaces which includes classifying spaces of compact Lie groups and their homotopical analogues. Moreover, we investigate their relationship in this context with other relevant functors in the analysis of the mod $p$ homotopy, such as Bousfield-Kan completion and Bousfield homological localization.

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