The splitting of the de Rham cohomology of soft function algebras is multiplicative

I. Baskov

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences

Abstract: Let $A$ be a real soft function algebra. In [1] we have obtained a canonical splitting $\mathrm{H}^* (\Omega ^\bullet _{A|\mathbb{R}}) \cong \mathrm{H}^* (X,\mathbb{R})\oplus \text{(something)}$ via the canonical maps $\Lambda_A:\mathrm{H} ^* (X,\mathbb{R})\to\mathrm{H} ^* (\Omega ^\bullet _{A|\mathbb{R}})$ and $\Psi_A:\mathrm{H} ^* (\Omega ^\bullet _{A|\mathbb{R}})\to\mathrm{H} ^* (X,\mathbb{R})$. In this paper we prove that these maps are multiplicative.

Key words and phrases: de Rham cohomology of algebras, soft function algebra, canonical splitting.

UDC: 515.142.217

Received: 18.09.2025

Language: English