Objective The aim of the project is to develop a new algorithmic approach to low-dimensional topology, low-dimensional variation functional, combinatorial group theory and, most important, to the investigation of the interaction between these subjects. This includes algorithmic investigation of extreme networks for general variation functional, generalizations, algorithmic enumeration of weighted minimal networks, and application to constructing hyperbolic structures on 3-manifolds with total boundaries. Algorithms for enumerating hyperbolic 3-manifolds, calculating Heegaard genera of 3-manifolds, detecting unknots. This involves both the theoretical investigations in these matters as well as writing the corresponding computer programs.The investigation of finitely presented groups and 2-dimensional complexes will concentrate on the relation gap problem, the relative Andrews-Curtis conjecture, algorithmically accessible bias-invariants, and the investigation of the interaction between multiparameter quantum groups, quantum invariants for 2-dimensional complexes and 3-manifolds. The project is based on the rather wide ranging modern research in this area previously worked out by teams in Chelyabinsk, Frankfurt, Edinburgh, Moscow, and Amsterdam.The results will be published in mathematical journals and reported on different conferences. Several of these are already being organized. Almost all participants of the project will meet during the May 1999 International Conference (Moscow State University) where a section devoted to algorithmic methods and variation problems, topology and group theory will be arranged. The results and perspectives will be discussed also at the Chelyabinsk International Conference and several short-time visits of NIS participants to Amsterdam, Frankfurt and vise-versa. The computer programs written during the project will be broadly distributed as share-ware with corresponding instructions, and will be useful for specialists. The more widely useful, such as programs for generating examples of knots and three manifolds nad calculating their invariants will also be incorporated in future versions of the electronic CDROM edition of the encyclopaedia of mathematics. Programme(s) IC-INTAS - International Association for the promotion of cooperation with scientists from the independent states of the former Soviet Union (INTAS), 1993- Topic(s) 2 - Mathematics, Telecommunications, Information Technologies INTAS - INTAS Call for proposal Data not available Funding Scheme Data not available Coordinator CWI, Stichting Mathematisch Centrum EU contribution No data Address Kruislaan 413 1098 SJ Amsterdam Netherlands See on map Total cost No data Participants (3) Sort alphabetically Sort by EU Contribution Expand all Collapse all Chelyabinsk State University Russia EU contribution No data Address ul. Br. Kashirinykh 129 454136 Chelyabinsk See on map Total cost No data M.V. Lomonosov Moscow State University Russia EU contribution No data Address Vorobyovy Gory 119899 Moscow See on map Total cost No data Universität Frankfurt Germany EU contribution No data Address Robert-Mayer-Strasse 6-10 60054 Frankfurt am Main See on map Total cost No data