TY - UNPB
T1 - De Rham algebras of closed quasiregularly elliptic manifolds are Euclidean
AU - Heikkilä, Susanna Anneli
AU - Pankka, Pekka
PY - 2023/2/22
Y1 - 2023/2/22
N2 - We show that, if a closed, connected, and oriented Riemannian $n$-manifold $N$ admits a non-constant quasiregular mapping from the Euclidean $n$-space $\mathbb{R}^n$, then the de Rham cohomology algebra $H_{\mathrm{dR}}^*(N)$ of $N$ embeds into the exterior algebra ${\bigwedge}^*\mathbb{R}^n$. As a consequence, we obtain a homeomorphic classification of closed simply connected quasiregularly elliptic $4$-manifolds.
AB - We show that, if a closed, connected, and oriented Riemannian $n$-manifold $N$ admits a non-constant quasiregular mapping from the Euclidean $n$-space $\mathbb{R}^n$, then the de Rham cohomology algebra $H_{\mathrm{dR}}^*(N)$ of $N$ embeds into the exterior algebra ${\bigwedge}^*\mathbb{R}^n$. As a consequence, we obtain a homeomorphic classification of closed simply connected quasiregularly elliptic $4$-manifolds.
UR - https://arxiv.org/abs/2302.11440
M3 - Preprint
BT - De Rham algebras of closed quasiregularly elliptic manifolds are Euclidean
ER -