The Homotopy 3-Type of Abelian C*-Algebras

Gregory Faurot; Giovanni Ferrer

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arXiv · 2603.29985

The Homotopy 3-Type of Abelian C*-Algebras

Gregory Faurot·Giovanni Ferrer

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Abstract

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 $T$.

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Gregory Faurot, Giovanni Ferrer. 2026-03-31. The Homotopy 3-Type of Abelian C*-Algebras. https://arxiv.org/abs/2603.29985

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