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Geometry and Topology of Open Manifolds

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 unders... ver más

31/01/2018

UGA

998K€

Presupuesto del proyecto: 998K€

Líder del proyecto

UGA-Université Grenoble Alpes No se ha especificado una descripción o un objeto social para esta compañía.

Fecha límite participación Sin fecha límite de participación.

Ver 2 Participantes

Financiación concedida El organismo FP7 notifico la concesión del proyecto el día 2018-01-31 No tenemos la información de la convocatoria

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2 Participantes

UGA

998.28K€ | Lider

UJF

N.D. | Participante

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Líder del proyecto

UGA-Université Grenoble Alpes No se ha especificado una descripción o un objeto social para esta compañía.

Presupuesto del proyecto 998K€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto 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.

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