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.