2-3-AUT

"Surfaces, 3-manifolds and automorphism groups"

Coordinatore	KOBENHAVNS UNIVERSITET    more Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie.
Nazionalità Coordinatore	Denmark [DK]
Totale costo	724˙992 €
EC contributo	724˙992 €
Programma	FP7-IDEAS-ERC Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
Code Call	ERC-2009-StG
Funding Scheme	ERC-SG
Anno di inizio	2009
Periodo (anno-mese-giorno)	2009-11-01   -   2014-10-31

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	KOBENHAVNS UNIVERSITET	DK	hostInstitution	724˙992.00
2	KOBENHAVNS UNIVERSITET	DK	hostInstitution	724˙992.00

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 Obiettivo del progetto (Objective)

'The scientific goal of the proposal is to answer central questions related to diffeomorphism groups of manifolds of dimension 2 and 3, and to their deformation invariant analogs, the mapping class groups. While the classification of surfaces has been known for more than a century, their automorphism groups have yet to be fully understood. Even less is known about diffeomorphisms of 3-manifolds despite much interest, and the objects here have only been classified recently, by the breakthrough work of Perelman on the Poincar'e and geometrization conjectures. In dimension 2, I will focus on the relationship between mapping class groups and topological conformal field theories, with applications to Hochschild homology. In dimension 3, I propose to compute the stable homology of classifying spaces of diffeomorphism groups and mapping class groups, as well as study the homotopy type of the space of diffeomorphisms. I propose moreover to establish homological stability theorems in the wider context of automorphism groups and more general families of groups. The project combines breakthrough methods from homotopy theory with methods from differential and geometric topology. The research team will consist of 3 PhD students, and 4 postdocs, which I will lead.'