Objective Research objectives and content The purpose of the project is to prove that the Floer homology of the cotangent bundle of a Riemannian manifold M is naturally isomorphic to the homology of the loop space. The main step of the proof is to obtain the gradient flow of the classical action functional on the loop space of M as an adiabatic limit of the Floer gradient flow of the symplectic action on the loop space of T*M. The limit is one where the metric on the momentum coordinate converges to zero. There is a natural correspondence between the critical points in both theories (perturbed geodesics) and the limit argument relates the heat flow of the classical action to perturbed J-holomorphic curves in the cotangent bundle. We intend to investigate implications of our result to - existence of Lagrangian submanifolds - spectral geometry Training content (objective, benefit and expected impact) Carrying out this project in collaboration with one of the leading experts in the field will give me detailed knowledge of analyzing nonlinear partial differential equations - a topic of fundamental interest in pure mathematics as well as in theoretical physics. The one-year symposium on symplectic geometry at Warwick university provides direct contact and access to researchers as well as research in symplectic geometry. Fields of science natural sciencesmathematicspure mathematicstopologysymplectic topologynatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equationsnatural sciencesphysical sciencestheoretical physics 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 UNIVERSITY OF WARWICK Address Gibbet hill road CV4 7AL Coventry United Kingdom See on map EU contribution € 0,00 Participants (1) Sort alphabetically Sort by EU Contribution Expand all Collapse all Not available Germany EU contribution € 0,00 Address See on map
