C. Li - Classifying sufficiently connected PSC manifolds in 4 and 5 dimensions
- document 1 document 2 document 3
- niveau 1 niveau 2 niveau 3
- audio 1 audio 2 audio 3
Descriptif
In this talk, I will discuss some recent developments on the topology of closed manifolds admitting Riemannian metrics of positive scalar curvature. In particular, we will prove if a closed PSC manifold of dimension 4 (resp. 5) has vanishing π2 (resp. vanishing π2 and π3), then a finite cover of it is homotopy equivalent to Snor connected sums of Sn-1 x S1. This extends a previous theorem on the non-existence of Riemannian metrics of positive scalar curvature on aspherical manifolds in 4 and 5 dimensions, due to Chodosh and myself and independently Gromov. A key step in the proof is a homological filling estimate in sufficiently connected PSC manifolds. This is based on joint work with Otis Chodosh and Yevgeny Liokumovich.
Intervenant
Thème
Notice
Documentation
Dans la même collection
-
J. Fine - Knots, minimal surfaces and J-holomorphic curvesFineJoël
I will describe work in progress, parts of which are joint with Marcelo Alves. Let L be a knot or link in the 3-sphere. I will explain how one can count minimal surfaces in hyperbolic 4-space
-
D. Tewodrose - Limits of Riemannian manifolds satisfying a uniform Kato conditionTewodroseDavid
Presentation of a joint work with G. Carron and I. Mondello where we study Kato limit spaces.
-
D. Stern - Harmonic map methods in spectral geometrySternDaniel
Over the last fifty years, the problem of finding sharp upper bounds for area-normalized Laplacian eigenvalues on closed surfaces has attracted the attention of many geometers, due in part to
-
M. Lesourd - Positive Scalar Curvature on Noncompact Manifolds and the Positive Mass TheoremLesourdMartin
The study of positive scalar curvature on noncompact manifolds has seen significant progress in the last few years. A major role has been played by Gromov's results and conjectures, and in
-
P. Burkhardt - Pointwise lower scalar curvature bounds for C0 metrics via regularizing Ricci flowBurkhardt-GuimPaula
We propose a class of local definitions of weak lower scalar curvature bounds that is well defined for C0 metrics. We show the following: that our definitions are stable under greater-than-second
-
J. Wang - Topological rigidity and positive scalar curvatureWangJian
In this talk, we shall describe some topological rigidity and its relationship with positive scalar curvature. Precisely, we will present a proof that a complete contractible 3-manifold with
-
D. Semola - Boundary regularity and stability under lower Ricci boundsSemolaDaniele
The theory of non smooth spaces with lower Ricci Curvature bounds has undergone huge developments in the last thirty years. On the one hand the impetus came from Gromov’s precompactness theorem
-
A. Mondino - Time-like Ricci curvature bounds via optimal transportMondinoAndrea
The goal of the talk is to present a recent work in collaboration with Cavalletti (SISSA) on optimal transport in Lorentzian synthetic spaces. The aim is to set up a “Lorentzian analog” of the
-
Y. Lai - A family of 3d steady gradient Ricci solitons that are flying wingsLaiYi
We find a family of 3d steady gradient Ricci solitons that are flying wings. This verifies a conjecture by Hamilton. For a 3d flying wing, we show that the scalar curvature does not vanish at
-
R. Perales - Recent Intrinsic Flat Convergence TheoremsPeralesRaquel
Théorèmes récents de convergence plane intrinsèque
-
R. Bamler - Compactness and partial regularity theory of Ricci flows in higher dimensionsBamlerRichard H.
We present a new compactness theory of Ricci flows. This theory states that any sequence of Ricci flows that is pointed in an appropriate sense, subsequentially converges to a synthetic flow.
-
F. Schulze - Mean curvature flow with generic initial dataSchulzeFelix
Mean curvature flow is the gradient flow of the area functional and constitutes a natural geometric heat equation on the space of hypersurfaces in an ambient Riemannian manifold. It is believed,
Sur le même thème
-
"Le mathématicien Petre (Pierre) Sergescu, historien des sciences, personnalité du XXe siècle"HerléaAlexandre
Alexandre HERLEA est membre de la section « Sciences, histoire des sciences et des techniques et archéologie industrielle » du CTHS. Professeur émérite des universités, membre effectif de l'Académie
-
Webinaire sur la rédaction des PGDLouvetViolaine
Rédaction des Plans de Gestion de Données (PGD) sous l’angle des besoins de la communauté mathématique.
-
Alexandre Booms : « Usage de matériel pédagogique adapté en géométrie : une transposition à interro…
« Usage de matériel pédagogique adapté en géométrie : une transposition à interroger ». Alexandre Booms, doctorant (Université de Reims Champagne-Ardenne - Cérep UR 4692)
-
J. Fine - Knots, minimal surfaces and J-holomorphic curvesFineJoël
I will describe work in progress, parts of which are joint with Marcelo Alves. Let L be a knot or link in the 3-sphere. I will explain how one can count minimal surfaces in hyperbolic 4-space
-
D. Tewodrose - Limits of Riemannian manifolds satisfying a uniform Kato conditionTewodroseDavid
Presentation of a joint work with G. Carron and I. Mondello where we study Kato limit spaces.
-
D. Stern - Harmonic map methods in spectral geometrySternDaniel
Over the last fifty years, the problem of finding sharp upper bounds for area-normalized Laplacian eigenvalues on closed surfaces has attracted the attention of many geometers, due in part to
-
M. Lesourd - Positive Scalar Curvature on Noncompact Manifolds and the Positive Mass TheoremLesourdMartin
The study of positive scalar curvature on noncompact manifolds has seen significant progress in the last few years. A major role has been played by Gromov's results and conjectures, and in
-
P. Burkhardt - Pointwise lower scalar curvature bounds for C0 metrics via regularizing Ricci flowBurkhardt-GuimPaula
We propose a class of local definitions of weak lower scalar curvature bounds that is well defined for C0 metrics. We show the following: that our definitions are stable under greater-than-second
-
J. Wang - Topological rigidity and positive scalar curvatureWangJian
In this talk, we shall describe some topological rigidity and its relationship with positive scalar curvature. Precisely, we will present a proof that a complete contractible 3-manifold with
-
D. Semola - Boundary regularity and stability under lower Ricci boundsSemolaDaniele
The theory of non smooth spaces with lower Ricci Curvature bounds has undergone huge developments in the last thirty years. On the one hand the impetus came from Gromov’s precompactness theorem
-
A. Mondino - Time-like Ricci curvature bounds via optimal transportMondinoAndrea
The goal of the talk is to present a recent work in collaboration with Cavalletti (SISSA) on optimal transport in Lorentzian synthetic spaces. The aim is to set up a “Lorentzian analog” of the
-
Y. Lai - A family of 3d steady gradient Ricci solitons that are flying wingsLaiYi
We find a family of 3d steady gradient Ricci solitons that are flying wings. This verifies a conjecture by Hamilton. For a 3d flying wing, we show that the scalar curvature does not vanish at
