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

1 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

Mathematics(all)
Applied Mathematics

Keywords

3-manifolds
Open manifolds
Ricci flow
Scalar curvature

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10.4171/JEMS/1008

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title = "Deforming 3-manifolds of bounded geometry and uniformly positive scalar curvature",

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.}",

note = "Funding Information: Acknowledgments. This research was partially supported by the Agence Nationale de la Recherche through project GTO ANR-12-BS01-0014. The second author is supported by the ERC Advanced Grant 320939, GETOM (GEometry and Topology of Open Manifolds). The fourth author was partially supported by the National Science Foundation grant NSF-DMS-1509027. Publisher Copyright: {\textcopyright} European Mathematical Society 2021",

year = "2021",

doi = "10.4171/JEMS/1008",

language = "English (US)",

volume = "23",

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journal = "Journal of the European Mathematical Society",

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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 - Funding Information: Acknowledgments. This research was partially supported by the Agence Nationale de la Recherche through project GTO ANR-12-BS01-0014. The second author is supported by the ERC Advanced Grant 320939, GETOM (GEometry and Topology of Open Manifolds). The fourth author was partially supported by the National Science Foundation grant NSF-DMS-1509027. 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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VL - 23

SP - 153

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

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