Braid groups and the jones polynomial in arbitrary 3-manifolds

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Project objective

The project is concerned with the construction of Jones-type invariants of knots in arbitrary 3-manifolds using and developing algebraic techniques analogous to Jones' original ones for the 3-sphere. It continues my current HCM project, in which I succeeded in constructing all such knot invariants in a solid torus, and then extended this construction to the lens spaces L(p,l) (as it had been proposed). For extending the construction to arbitrary 3-manifolds, the following has been done: I have established the necessary knot-theoretical background as well as the existence of associated braid structures in 3-manifolds, and also proved braid isotopy theorems. The method used for L(p,l) seems to be the appropriate one for resolving the problem in the general case. one of the objectives of the project is to provide a unifying understanding of the Jones-Witten theory in 3-manifolds. As this is a proposal for a Return Fellowship, I wish to add that in parallel to my research project I plan to set up in Athens a postgraduate course in Knot theory, the Jones polynomial and its connections to Statistical Mechanics and Biology. I shall also give a seminar series on my research work and organise a Low-Dimensional Topology conference in Greece (with Professor V.F.R. Jones as a co-organiser).

Original text from CORDIS.

Participants

• NATIONAL AND KAPODISTRIAN UNIVERSITY OF ATHENS · ATHENSCoordinatorGreece
• Not availableCity levelGreece

Links

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