The generalization of the traditional notion to symplectomorphism group of a symplectic manifold to n-plectic spaces in higher geometry
For $\mathbf{H}$ a cohesive (∞,1)-topos equipped with differential cohesion, let $\mathbb{G} \in Grp(\mathbf{H})$ by an ∞-group equipped with braided ∞-group structure. Write $\mathbf{B}\mathbb{G}_{conn}$ for the corresponding moduli ∞-stack of $\mathbb{G}$-principal ∞-connections (see there). For $\nabla \;\colon\; X \to \mathbf{B}\mathbb{G}_{conn}$ a $\mathbb{G}$-principal ∞-connection on some object $X \in \mathbf{H}$, which here we call a prequantum ∞-bundle. the corresponding quantomorphism ∞-group by definition comes with a canonical homomorphism
to the automorphism ∞-group of $X$. The Hamiltonian symplectomorphism $\infty$-group $\mathbf{HamSym}(\nabla)$ is the 1-image of this map
higher and integrated Kostant-Souriau extensions:
(∞-group extension of ∞-group of bisections of higher Atiyah groupoid for $\mathbb{G}$-principal ∞-connection)
(extension are listed for sufficiently connected $X$)
Domenico Fiorenza, Chris Rogers, Urs Schreiber, Higher prequantum geometry?
Last revised on November 2, 2022 at 20:40:23. See the history of this page for a list of all contributions to it.