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.
Fields of science (EuroSciVoc)
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Programme(s)
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Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
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Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Call for proposal
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Funding Scheme
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Coordinator
1098 SJ Amsterdam
Netherlands
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.