Objective Research objectives and content The purpose of my research project is to investigate the connection between the topology and geometry of 3-dimensional manifolds and the algebraic and analytic properties of their representation spaces. The main part of the project deals with the exploration of the link between analytic and algebraic-topological methods. The gauge theory plays a central role in my project because it provides the connection between topology and analysis. My objective is to find an algebraic and topological interpretation of invariants of 3-dimensional rnanifolds which are defined via gauge theory (e.g. Chern-Simons invariant and Floer homology). More precisely, two key goals are, firstly to find an extension of Casson's invariant for 3-dimensional manifolds with boundary and secondly to give an algebraic-topological interpretation of the Jones polynomial are other aims of my project. Besides this principal project my host Michel Boileau (Pr University), Joan Poni (CR CNRS) and myself plan to engage on a common research project. The aim of the common project is to prove Thurston's orbifold conjecture at worst in some special cases. Training content (objective, benefit and expected impact) The training will enable me to present my "Habilitation" at the Universitat-Gesamthochschule-Siegen. Therefore, I expect the training should have a strong positive impact on the prospects of my career. I am sure I will benefit from the daily contact with the specialists already working in Toulouse. Fields of science natural sciencesmathematicspure mathematicstopologynatural sciencesmathematicspure mathematicsgeometry Programme(s) FP4-TMR - Specific research and technological development programme in the field of the training and mobility of researchers, 1994-1998 Topic(s) 0302 - Post-doctoral research training grants TM22 - Geometry and Topology Call for proposal Data not available Funding Scheme RGI - Research grants (individual fellowships) Coordinator UNIVERSITE PAUL SABATIER DE TOULOUSE III EU contribution No data Address 118,Route de Narbonne 118 31062 TOULOUSE France See on map Total cost No data Participants (1) Sort alphabetically Sort by EU Contribution Expand all Collapse all Not available Germany EU contribution No data Address See on map Total cost No data
