On triples of ideal chambers in A2-buildings

Anne Parreau (1)

1 IF - Institut Fourier

We investigate the geometry in a real Euclidean building X of type A2 of some simple configurations in the associated projective plane at infinity P, seen as ideal configurations in X, and relate it with the projective invariants (from the cross ratio on P). In particular we establish a geometric classification of generic triples of ideal chambers of X and relate it with the triple ratio of triples of flags.

Domaines: Mathématiques [math]; Topologie géométrique [math.GT]

Anne Parreau. On triples of ideal chambers in A2-buildings. Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial, 2019, 17 (2), pp.109-140. ⟨10.2140/iig.2019.17.109⟩. ⟨hal-01138345v2⟩