De Rham algebras of closed quasiregularly elliptic manifolds are Euclidean

• 成果类型: Article
• 署名作者: Heikkila, Susanna; Pankka, Pekka
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2025.201.2.3
• 发表日期: 2025
• 页码: 459-488
• 关键词: quasi-regular mappings

摘要

We show that, if a closed, connected, and oriented Riemannian n-manifold N admits a non-constant quasiregular mapping from the Euclidean nspace Rn, then the de Rham cohomology algebra H & lowast;dR(N) of N embeds into the exterior algebra n & lowast;Rn. As a consequence, we obtain a homeomorphic classification of closed simply connected quasiregularly elliptic 4-manifolds.