QUANTUM TOPOLOGY · Quantum topology and 3-manifolds

Lines connect the coordinator with its partners.

Project objective

This Proposal is a Project for a long-term professional reintegration of the Applicant in his home country at the Laboratoire Emile Picard de Mathéma- tiques, University of Toulouse III, France. The Project is fully endorsed by the Host Institution. Quantu m Topology in dimension 3 is a recent and rapidly-growing field at the intersection of Topology and Mathematical Physics. The Proposal seeks to develop new topologica! quantum field theories associated with 3-manifolds endowed with complex spin structures in order to bridge the gap between quan- tum invariants and their topological or geometrical interpretation. Some of the necessary tools were previously developped under a Marie Curie Fellowship. The Project includes the full algebraic classification (as o pposed to Witt- classification) of complex spin structures on 3-manifolds and the generalization of the Kontsevitch integral (LMO invariant) to complex spin structures. The Project provides a unifying framework for topological invariants of complex spin st ructures on 3-manifolds, including finite-type, quantum and Gauss di- agram invariants.

Original text from CORDIS.

Participants

• UNIVERSITE PAUL SABATIER-TOULOUSE III · TOULOUSECoordinatorFrance

Links

• View on CORDIS