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Generalized geometry: 3-manifolds and applications

Objective

Generalized geometry is a revolutionary approach to geometric structures pioneered by Hitchin in 2003, soon becoming an active topic catching the interest and bringing together the expertise of geometers and theoretical physicists. Generalized complex structures, defined for even-dimensional manifolds, are both a genuinely interesting mathematical structure, providing insight of complex and symplectic geometry, and the suitable notion for some physical theories like mirror symmetry. Odd-dimensional manifolds within generalized geometry have not been satisfactorily studied until the recent introduction of generalized geometry of type Bn and its study in my PhD thesis. There, the case of 3-manifolds drew special attention thanks to the recent Thurston's geometrization theorem and the fact that the type-change locus of a 3-manifold is a link, bringing in knot and link theory. This action combines the generalized geometry expertise of the experienced researcher with the host’s expertise on 3-manifold and knot and link theory in order to set a novel geometrical framework for structures on odd-dimensional manifolds, understand the case of 3-manifolds in depth, and create a two-way bridge between these previously unrelated areas, with innovative applications in both.

Field of science

  • /natural sciences/mathematics/pure mathematics/geometry

Call for proposal

H2020-MSCA-IF-2016
See other projects for this call

Funding Scheme

MSCA-IF-EF-ST - Standard EF

Coordinator

UNIVERSIDAD AUTONOMA DE BARCELONA
Address
Calle Campus Universitario Sn Cerdanyola V
08290 Cerdanyola Del Valles
Spain
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 170 121,60