Cohomology in algebra, geometry, physicsand statistics

Homogeneous 8-manifolds admitting invariant Spin(7)-structures

We study invariant Spin7-structures on 8-dimensional compact homogeneous spaces. We classify all simply-connected non-symmetric compact homogeneous spaces M = G/K of a compact almost effective Lie group G, which admit a G-invariant Spin7-structure and describe its type in terms of Fernández's classification. In some cases we also analyse the associated Spin7-connection with torsion.

This talk is based on a recent joint work with D. Alekseevsky, A. Fino and A. Raffero.