Cremona transformations and homeomorphisms of surfaces

János Kollár (1) , Frédéric Mangolte (2)

1 Princeton University
2 LAMA - Laboratoire de Mathématiques

We show that the action of Cremona transformations on the real points of quadrics exhibits the full complexity of the homeomorphisms of the sphere and of all non-orientable surfaces. The main result says that if X is rational, then Aut(X), the group of algebraic automorphisms, is dense in Homeo(X), the group of self-homeomorphisms of X.

Domaines: Géométrie algébrique [math.AG]; Topologie géométrique [math.GT]

János Kollár, Frédéric Mangolte. Cremona transformations and homeomorphisms of surfaces. 2008. ⟨hal-00323333v1⟩