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Geometry and Topology of Open Manifolds

Cel

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 programme has already been highly successful in the compact case whereas basic questions are not answered in the open case. The key tool which ought to be used in the three items is the Ricci flow with bubbling off, in dimension 3, described by myself and my collaborators. This opened the way to applying Ricci flow to non-compact manifolds and it is a breakthrough which gives a very optimistic approach to some deep conjectures. The study of Whitehead manifolds will open a wide realm of research since results are scarce. This will provide work for quite a few graduate students and for several years. My goal is to make such a significant progress that the subject will become proeminent in Riemannian Geometry. Again, for this the Ricci flow will be an unavoidable tool. Constructing explicit Riemannian metrics with various properties is another goal, which pertains to the same circle of ideas, and will lead to a systematic study of these spaces. This is a new and groundbreaking direction of research. I have already obtained some results in these direction and I intend to go much further and to enhance my national and international collaborations using the grant if accepted.

Zaproszenie do składania wniosków

ERC-2012-ADG_20120216
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System finansowania

ERC-AG - ERC Advanced Grant

Instytucja przyjmująca

UGA-Université Grenoble Alpes
Wkład UE
€ 998 276,80
Adres
621, AVENUE CENTRALE
38401 SAINT MARTIN D'HERES
Francja

Zobacz na mapie

Region
RUP FR — Régions Ultrapériphériques Françaises Guadeloupe Guadeloupe
Rodzaj działalności
Higher or Secondary Education Establishments
Kontakt administracyjny
Aurélie Diringer-Dagorne (Ms.)
Kierownik naukowy
Gérard Robert Besson (Dr.)
Linki
Koszt całkowity
Brak danych

Beneficjenci (2)