Geometric structures on 3-manifolds (GEOMSTRUCT3MFDS)

RESEARCH FIELD: Geometry and Topology od 3-manifolds (from now on3-mfds).OBJECTIVES: To contribute to the study and classifications of 3-mfds. More precisely: To study geoemtric properties of 3-mfds. To develop the technique of Idela Triangulations and hyperbolicity equations. To develop efficient algorithms to recognize 3-mfds. To study Representations of the fundamental group of 3-mfds into the isometries of the hyperbolic space.RELEVANCE: Low-dimenaional topology is one of the hottest field in contemporary Mathematics. Recent results, like the solution of the Poincare Conjecture (one of the one milion dollar prize problems), open the way to classifications of 3-mfds and put this field in a leading position in the scenario of international research. INTERDISCIPLINARITY: This project has many connections with Algebraic Geometry and Analysis. Connections with gravitational problems strongly link the project-investigations to Physics. MOBILITY OBJECTIVES: To increase the scientific independence of the applicant, to put it in contact with leading research groups in Europe, to consolidate and enforce his role in the enviroment of International Research. To facilitate transfer of knowledge between European scientists. To create new links between European Research Centres.