arXiv subjects

Gabriel Sevestre

Publications and source records attributed to Gabriel Sevestre.

2 recordsLinked to original sources

arXiv2021

On the prequantisation map for 2-plectic manifolds

For a manifold $M$ with an integral closed 3-form $ω$, we construct a $PU(H)$-bundle and a Lie groupoid over its total space, together with a curving in the sense of gerbes. If the form is non-degenerate, we furthermore give a natural Lie 2-algebra quasi-isomorphism from the observables of $(M,ω)$ to the weak symmetries of the above geometric structure, generalising the prequantisation map of Kostant and Souriau.

math.DG↗

arXiv2018

Lagrangian submanifolds of standard multisymplectic manifolds

We give a detailed, self-contained proof of Geoffrey Martin's normal form theorem for Lagrangian submanifolds of standard multisymplectic manifolds (that generalises Alan Weinstein's famous normal form theorem in symplectic geometry), providing also complete proofs for the necessary results in foliated differential topology, i.e., a foliated tubular neighborhood theorem and a foliated relative Poincaré lemma.

math.DG↗