Deforming 3-manifolds of bounded geometry and uniformly positive scalar curvature

Laurent Bessières; Gérard Besson; Sylvain Maillot; Fernando C. Marques

doi:10.4171/jems/1008

JournalsjemsVol. 23, No. 1pp. 153–184

Deforming 3-manifolds of bounded geometry and uniformly positive scalar curvature

Laurent Bessières
Université de Bordeaux, Talence, France
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Gérard Besson
Université Grenoble Alpes, Gières, France
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Sylvain Maillot
Université de Montpellier 2, France
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Fernando C. Marques
Princeton University, USA
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Abstract

We prove that the moduli space of complete Riemannian metrics of bounded geometry and uniformly positive scalar curvature on an orientable 3-manifold is path-connected. This generalises the main result of the fourth author [Mar12] in the compact case. The proof uses Ricci flow with surgery as well as arguments involving performing infinite connected sums with control on the geometry.

Cite this article

Laurent Bessières, Gérard Besson, Sylvain Maillot, Fernando C. Marques, Deforming 3-manifolds of bounded geometry and uniformly positive scalar curvature. J. Eur. Math. Soc. 23 (2021), no. 1, pp. 153–184

DOI 10.4171/JEMS/1008