Objective
The research topic we propose lies in the intersection of Group Theory, Geometry and (low-dimensional) Topology. In this project we wish to explore the geometry and the topology at infinity of discrete groups. The geometrical viewpoint for groups has sparked the interest of geometers, topologists and group theorists since the seminal work of M.Gromov on the asymptotic invariants of groups. We would like to look at groups from a topological viewpoint, and to study some topological properties (at infinity) of groups. In particular we will mainly focus on the geometric simple connectivity (g.s.c.) and the simple connectivity at infinity. The simple connectivity at infinity is an important tameness condition on the ends of the space, and it has been used to characterize Euclidean spaces among contractible open topological manifolds. Whereas the geometric simple connectivity is a related notion developed by V.Poenaru (mostly in dimensions 3 and 4), in his work concerning the Poincaré Conjecture. It is worthy to note that it can be shown that all reasonable examples of groups (e.g. word hyperbolic, semi-hyperbolic, CAT(0), group extensions, one relator groups) are g.s.c. Hence it would be very interesting to find an example of a finitely presented group which fails to be g.s.c. Discrete groups which are not g.s.c. (if they exist) would lay at the opposite extreme to hyperbolic (or CAT(0)) groups and thus they should be non generic, in a probabilistic sense. The first step will be to find some combinatorial property equivalent to the g.s.c. On the other hand, if one can show that ANY group is geometrically simply connected, then the g.s.c. would be the first non-trivial property which holds true for all groups (contradicting the underlying philosophy of the Geometric Group Theory). Both cases will have a deep impact in the understanding of the space of groups and for their (geometrical) classification.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics pure mathematics topology
- natural sciences mathematics pure mathematics geometry
- humanities philosophy, ethics and religion philosophy
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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
FP7-PEOPLE-IEF-2008
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Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Coordinator
91405 ORSAY CEDEX
France
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.