The Cantor Riemannium

Ricardo Pérez-Marco (1, 2, 3)

1 CNRS - Centre National de la Recherche Scientifique
2 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
3 SU - Sorbonne Université

The Riemann surface of a holomorphic germ is the space generated by its Weierstrass analytic continuation. The Riemannium space of a holomorphic germ is the space generated by its Borel monogenic continuation. Riemannium spaces are metric, path connected, Gromov length spaces, not necessarily σ-compact. We construct an example of Riemannium space: The Cantor Riemannium.

Domaines: Variables complexes [math.CV]; Topologie algébrique [math.AT]; Géométrie différentielle [math.DG]

Ricardo Pérez-Marco. The Cantor Riemannium. 2020. ⟨hal-02552146v2⟩