arXiv subjects

Gregory Faurot

Publications and source records attributed to Gregory Faurot.

3 recordsLinked to original sources

arXiv2026

The Homotopy 3-Type of Abelian C*-Algebras

We compute the homotopy groups at each unital abelian C*-algebra $C(T)$ in the Morita $3$-category of abelian C*-algebras, C*-algebras with central maps, C*-correspondences, and adjointable bimodule maps. We describe these groups in terms of the topological data of the underlying compact Hausdorff space $T$. We also compute the actions of the first homotopy group on the second and third homotopy groups in terms of these topological invariants of $T$.

math.OA↗

arXiv2025

$\mathcal{Z}$-stable Graph Algebras

We introduce a divisibility-type condition for directed graphs that is necessary for $\mathcal{Z}$-stability of the corresponding graph $C^*$-algebra. We prove that this condition is sufficient if either the graph $E$ has no cycles or the algebra $C^*(E)$ has finitely many ideals. Under the further assumption that $E$ is a finite graph, we provide a complete characterization of $\mathcal{Z}$-stability of $C^*(E)$. We conjecture that our divisibility condition and Condition (K) are equivalent to $\mathcal{Z}$-stability of the graph algebra. We prove that it is equivalent to $C^*(E)$ being pure, verifying the Generalized Toms--Winter Conjecture for graph algebras with finitely many ideals.

math.OA↗

arXiv2023

Nuclear dimension of graph C$^*$-algebras with Condition~(K)

We prove that for any countable directed graph $E$ with Condition~(K), the associated graph $C^*$-algebra $C^*(E)$ has nuclear dimension at most $2$. Furthermore, we provide a sufficient condition producing an upper bound of $1$.

math.OA↗