# GTO - Géométrie et Topologie des variétés Ouvertes

## Project ANR-12-BS01-0004

GTO is a research project founded by Agence Nationale de la Recherche, 2013-2016.
Coordinator : Sylvain Maillot

#### Presentation

The purpose of this project is to study the interactions between Riemannian Geometry and the topology of open manifolds. A general question is to find the best Riemannian metric on a given manifold; a related question is to understand the topological consequences of the existence of a metric with given properties. This program has already been highly successful in the compact case whereas basic questions are not answered in the open case. The members of this project share a common interest for open manifolds, and study them using different approaches and techniques.
The project team is divided into three nodes : Montpellier (coord. Sylvain Maillot), Grenoble (coord. Gérard Besson), and Nantes (coord. Gilles Carron).
The other participants are Michel Boileau (Marseille), Laurent Bessières (Bordeaux), Zindine Djadli (Grenoble), Marc Herzlich (Montpellier), Vincent Minerbe (Paris 6), and Samuel Tapie (Nantes).
The 2-year postdoctoral position funded by the project is held by Daniel Ramos.

#### Activities

The first meeting of the project team took place in Grenoble from March 27 to March 29, 2013. There were many informal discussions and a few formal talks, mostly surveys of recent research related to the project themes.
The programme was the following:

Gilles Carron: Courbure scalaire positive, d'après Gromov-Lawson, Weinberger et al.

Gérard Besson: La variété de Whitehead

Samuel Tapie: La conjecture de Marden, d'après Thurston, Bonahon, Agol, Gabai-Calegari

Sylvain Maillot: Exemples "exotiques" de variétés et d'orbifolds ouverts de dimension 3

The second meeting took place in Montpellier from November 20 to November 22, 2013. The programme can be found here.

The third meeting took place in Nantes from April 2 to April 4, 2014. The programme can be found here.

The fourth meeting, co-organized with the ERC project GETOM, took place in Grenoble from February 4 to February 6, 2015. The programme can be found here.

The next meeting is scheduled for autumn 2015 and will take place in Montpellier.

#### (Pre)publications

L. Bessières, G. Besson, and S. Maillot. Long time behavour of Ricci flow on open 3-manifolds. * Comm. Math. Helv., * to appear.
M. Boileau and S. Boyer. Graph manifolds which are Z-homology 3-spheres admit taut foliations. ArXiv : 1303.5264

V. Bour and G. Carron. A sphere theorem for three dimensional manifolds with integral pinched curvature. ArXiv : 1408.7091

G. Carron. Riesz transform on manifolds with quadratic curvature decay. ArXiv : 1403.6278

J. Cortier and V. Minerbe. On complete stationary vacuum initial data. ArXiv : 1402.0690

M. Herzlich. Universal positive mass theorems. ArXiv : 1401.6009

S. Maillot. An algorithmic classification of open surfaces. ArXiv
: 1209.2818

T. Roblin and S. Tapie. Moyennabilité et exposant critique. *Ens. Math.* 43 (2013)

P. Suarez-Serrrato and S. Tapie. Yamabe flows and extremal entropy on complete manifolds. Preprint du Max Planck Institute no 5201