Cohomology of spaces of Hopf equivariant maps of spheres

V.A. Vassiliev

Homology, homotopy, and applications, Tome 26 (2024) no. 2, pp. 219-227.

Résumé

For any natural numbers $k \leqslant n$, the rational cohomology ring of the space of continuous maps $S^{2k-1} \to S^{2n-1}$ (respectively, $S^{4k-1} \to S^{4n-1}$, which are equivariant under the Hopf action of the circle (respectively, of the group $S^3$ of unit quaternions), is naturally isomorphic to that of the Stiefel manifold $V_k (\mathbb{C}^n)$ (respectively, $V_k (\mathbb{H}^n))$. The natural maps of integral cohomology groups of these spaces of equivariant maps to cohomology of Stiefel manifolds are surjective but not injective.

Détail

DOI : 10.4310/HHA.2024.v26.n2.a11

Classification : 55P91, 55R91, 57R91
Keywords: equivariant map, configuration space, Stiefel manifold, spectral sequence