The classification of compact simply connected biquotients in dimension 6 and 7

Abstract

We classify all compact simply connected biquotients of dimension 6 and 7. For each $6$-dimensional biquotient, all pairs of groups $(G,H)$ and homomorphisms $H\to G\times G$ giving rise to it are classified.

Final version. To appear in Math. Ann

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• Positive curvature and torus symmetry in small dimensions, I -- Dimensions 10, 12, 14, and 16
• Positive Ricci curvature on simply-connected manifolds with cohomogeneity-two torus actions
• On geometric formality of rationally elliitic manifolds in dimensions $6$ and $7$