ASYMGTG

Asymptotic geometry and topology of discrete groups

 Coordinatore UNIVERSITE PARIS-SUD 

 Organization address address: RUE GEORGES CLEMENCEAU 15
city: ORSAY
postcode: 91405

contact info
Titolo: Mr.
Nome: Nicolas
Cognome: Lecompte
Email: send email
Telefono: +331 69 15 55 89
Fax: +331 69 15 55 99

 Nazionalità Coordinatore France [FR]
 Totale costo 0 €
 EC contributo 157˙279 €
 Programma FP7-PEOPLE
Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
 Code Call FP7-PEOPLE-IEF-2008
 Funding Scheme MC-IEF
 Anno di inizio 2009
 Periodo (anno-mese-giorno) 2009-09-01   -   2011-08-31

 Partecipanti

# participant  country  role  EC contrib. [€] 
1    UNIVERSITE PARIS-SUD

 Organization address address: RUE GEORGES CLEMENCEAU 15
city: ORSAY
postcode: 91405

contact info
Titolo: Mr.
Nome: Nicolas
Cognome: Lecompte
Email: send email
Telefono: +331 69 15 55 89
Fax: +331 69 15 55 99

FR (ORSAY) coordinator 157˙279.60

Mappa


 Word cloud

Esplora la "nuvola delle parole (Word Cloud) per avere un'idea di massima del progetto.

discrete    connectivity    space    property    viewpoint    topology    first    infinity    theory    cat    topological    geometrical    simple    group    geometry    hyperbolic    geometric    groups   

 Obiettivo del progetto (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.'

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