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

This paper focuses on $\mathrm{RCD}(0,2)$-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 $\mathrm{RCD}(0,2)$-structure. We then describe the moduli space of $\mathrm{RCD}(0,2)$-structures for each space and show that it is contractible.

Dans cet article, nous étudions les espaces $\mathrm{RCD}(0,2)$, 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 $\mathrm{RCD}(0,2)$. Nous décrivons ensuite l’espace de modules des structures $\mathrm{RCD}(0,2)$ 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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