BRSHADOWS · Branched shadows and invariants of smooth 4-manifolds

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Project objective

This application proposes a period of mobility to place a researcher currently developing his own long-term research plan into a leading international research group in the study of torsion and quantum invariants. The goals of the proposal are to complete applicants training on low dimensional topology, and to contribute new scientific results to the area. The scientific aim is to develop the theory of branched shadows of 4-manifolds through two applications: finding 2-cohomology classes satisfying adjunction inequalities (in particular Seiberg-Witten classes) and defining new Quantum Invariants. The first application will use the equality in the 3-dimensional case between torsion and Seiberg-Witten invariants which allows one to calculate the latter through branched spines. A combinatorial object based on branched shadows will be defined to find cohomology classes satisfying the adjunction inequalities in 4-manifolds. This object will represent a codimension 2 torsion and will be related to Seiberg-Witten invariants. The second application will be a generalization through branched shadows of the Quantum Hyperbolic Invariants defined by Baseilhac and Benedetti through branched spines. The objectives will be met by combining the hosts expert knowledge of the methods and techniques of torsions and quantum invariants with the researchers background knowledge on branched shadows. By joining one of the top international research teams in the field, experienced in providing training through research at all levels, the applicant will: learn new methods and techniques in the study of torsion and quantum groups, increase his involvement and enhance links with the community, diversify his expertise, particularly deepening his knowledge on Quantum Invariants. This will build on his existing knowledge providing essential complementary techniques, and thus allow him to complete his training in the theories of torsion and quantum invariants, and establish himself in?

Original text from CORDIS.

Participants

• UNIVERSITE LOUIS PASTEUR STRASBOURG · STRASBOURGCoordinatorCity levelFrance

Links

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