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

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

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

Mathematics

Research output: Contribution to journal › Review article › peer-review

2 Scopus citations

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.

Original language	English (US)
Pages (from-to)	153-184
Number of pages	32
Journal	Journal of the European Mathematical Society
Volume	23
Issue number	1
DOIs	https://doi.org/10.4171/JEMS/1008
State	Published - 2021

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

Keywords

3-manifolds
Open manifolds
Ricci flow
Scalar curvature

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10.4171/JEMS/1008

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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.",

keywords = "3-manifolds, Open manifolds, Ricci flow, Scalar curvature",

author = "Laurent Bessi{\`e}res and G{\'e}rard Besson and Sylvain Maillot and Marques, {Fernando C.}",

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year = "2021",

doi = "10.4171/JEMS/1008",

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T1 - Deforming 3-manifolds of bounded geometry and uniformly positive scalar curvature

AU - Bessières, Laurent

AU - Besson, Gérard

AU - Maillot, Sylvain

AU - Marques, Fernando C.

N1 - Publisher Copyright: © European Mathematical Society 2021

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - 3-manifolds

KW - Open manifolds

KW - Ricci flow

KW - Scalar curvature

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DO - 10.4171/JEMS/1008

M3 - Review article

AN - SCOPUS:85099056848

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EP - 184

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

IS - 1

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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