Explicit Quillen models for Cartesian products of $2$-cones

• Main Authors: Buijs, Urtzi, Carrasquel, José, Vandembroucq, Lucile
• Format: Journal Article
• Language: English
• Published: 28-02-2024
• Subjects: Mathematics - Algebraic Topology
• DOI: 10.48550/arxiv.2402.18168

We give an explicit minimal Quillen model for the Cartesian product $X\times
Y$ of rational $2$-cones in terms of derivations and a binary operation $\star
\colon \mathbb{M}(V)\otimes \mathbb{L}(W)\to \mathbb{L}(V\oplus W\oplus
s(V\otimes W))$, where $(\mathbb{L}(V), \partial)$ and $(\mathbb{L}(W),
\partial)$ are Quillen minimal models for $X$ and $Y$ respectively and
$\mathbb{M}$ denotes the free magma on $W$. The model presented also allows us
to explicitly describe a model for the diagonal map $\Delta \colon X\to X\times
X$.