On fibrations with flat fibres

Valentin Ovsienko (1) , Serge Tabachnikov (2)

1 ICJ - Institut Camille Jordan
2 Department of Mathematics

We describe the pairs (p, n) such that n-dimensional affine space is fibred by pairwise skew p-dimensional affine subspaces. The problem is closely related with the theorem of Adams on vector fields on spheres and the Hurwitz-Radon theory of composition of quadratic forms.

Domaines: Topologie algébrique [math.AT]

Valentin Ovsienko, Serge Tabachnikov. On fibrations with flat fibres. Bull. Lond. Math. Soc., 2013, 45 (3), pp.625--632. ⟨hal-00864643⟩