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Geometry and prequantisation of 2-plectic manifolds

Abstract : An ‘n-plectic manifold’ is a couple formed by a manifold and a closed, non-degenerate differentiable form of degree (n+1). These manifolds generalize the symplectic case (1-plectic) and give a natural framework for studying geometric classical field theories (as well as symplectic manifolds give a natural framework for studying classical mechanics). N-plectic manifolds, already studied since the 70’s, became paramount because of their role in the so-called ‘higher’ approach to differential geometry and topology, subtle structures related to category theory, freshly discovered. In this PhD thesis, we will study almost exclusively 2-plectic manifolds, notably distinguished submanifolds (Lagrangian, co-isotropic…), the dynamic of Hamiltonian systems and symetries of 2-plectic manifolds, as well as their prequantisation.
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Submitted on : Thursday, October 14, 2021 - 3:14:52 PM
Last modification on : Saturday, October 16, 2021 - 11:18:03 AM

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Gabriel Sevestre. Geometry and prequantisation of 2-plectic manifolds. Differential Geometry [math.DG]. Université de Lorraine, 2021. English. ⟨NNT : 2021LORR0142⟩. ⟨tel-03378218⟩

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