Objective The goal of this project is to study the topology of Stein manifolds from the viewpoint of symplectic and contact geometry. It addresses the fundamental questions of the subject: - How does the Lagrangian skeleton of a Stein manifold determine the Stein structure? - To what extent the study of Stein structures can be reduced to a combinatorial study of the skeleton? - How are the symplectic invariants of Stein manifolds, respectively the contact invariants of their boundary, determined by the skeleton? For the topological part, we will use as a source of inspiration the theory of spines and shadows of 3- and 4- manifolds. One of the goals of this research project is to adapt it to the setup of Stein manifolds and develop a calculus of Lagrangian shadows. Concerning invariants of contact manifolds, we aim to interpret symplectic homology of Stein manifolds and contact homology of their boundaries in topological terms, with the skeleton playing a central role. Further ramifications of this research project include the development of string topology on singular (stratified) spaces and the symplectic study of singularities. Fields of science natural sciencesmathematicspure mathematicstopologynatural sciencesmathematicspure mathematicsgeometry Programme(s) 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) Topic(s) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations Call for proposal ERC-2010-StG_20091028 See other projects for this call Funding Scheme ERC-SG - ERC Starting Grant Host institution CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS EU contribution € 942 921,07 Address RUE MICHEL ANGE 3 75794 Paris France See on map Region Ile-de-France Ile-de-France Paris Activity type Research Organisations Principal investigator Alexandru Oancea (Dr.) Administrative Contact Julie Zittel (Ms.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data Beneficiaries (2) Sort alphabetically Sort by EU Contribution Expand all Collapse all CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS France EU contribution € 942 921,07 Address RUE MICHEL ANGE 3 75794 Paris See on map Region Ile-de-France Ile-de-France Paris Activity type Research Organisations Principal investigator Alexandru Oancea (Dr.) Administrative Contact Julie Zittel (Ms.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data UNIVERSITE DE STRASBOURG Participation ended France EU contribution € 110 180,16 Address RUE BLAISE PASCAL 4 67081 Strasbourg See on map Region Grand Est Alsace Bas-Rhin Activity type Higher or Secondary Education Establishments Administrative Contact Sandrine Schott-Carriere (Ms.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data
