Contractibility of moduli spaces of RCD(0,2)-structures
Navarro, Dimitri1
1 12 Chemin des écoliers 69320 Feyzin (France)
Annales de l'Institut Fourier, Online first, 47 p.

This paper focuses on RCD(0,2)-spaces, i.e. possibly non-smooth metric measure spaces with nonnegative Ricci curvature and dimension at most 2. First, we establish a list of the compact topological spaces admitting an RCD(0,2)-structure. We then describe the moduli space of RCD(0,2)-structures for each space and show that it is contractible.

Dans cet article, nous étudions les espaces RCD(0,2), autrement dit les espaces métriques mesurés (potentiellement singuliers) de courbure de Ricci positive et de dimension au plus 2. Tout d’abord, nous établissons la liste des espaces topologiques compacts qui admettent une structure RCD(0,2). Nous décrivons ensuite l’espace de modules des structures RCD(0,2) pour chacun des éléments de la liste et nous montrons qu’il est contractile.

Received:
Revised:
Accepted:
Online First:
DOI: 10.5802/aif.3714
Classification: 51F99
Keywords: Metric Geometry, Ricci curvature, Topology, RCD spaces, Moduli Spaces
Mots-clés : Géométrie métrique, Courbure de Ricci, Topologie, Espaces RCD, Espace de modules

Navarro, Dimitri 1

1 12 Chemin des écoliers 69320 Feyzin (France) 
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Navarro, Dimitri. Contractibility of moduli spaces of RCD(0,2)-structures. Annales de l'Institut Fourier, Online first, 47 p.

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