Related papers: A cohomological framework for homotopy moment maps

Given a multisymplectic manifold $(M,\omega)$ and a Lie algebra $\frak{g}$ acting on it by infinitesimal symmetries, Fregier-Rogers-Zambon define a homotopy (co-)moment as an $L_{\infty}$-algebra-homomorphism from $\frak{g}$ to the…

Associated to any manifold equipped with a closed form of degree >1 is an `L-infinity algebra of observables' which acts as a higher/homotopy analog of the Poisson algebra of functions on a symplectic manifold. In order to study Lie group…

Consider a closed non-degenerate 3-form $\omega$ with an infinitesimal action of a Lie algebra $\mathfrak{g}$. Motivated by the fact that the observables associated to $\omega$ form a Lie 2-algebra, we introduce homotopy moment maps defined…

We introduce the notion of a weak (homotopy) moment map associated to a Lie group action on a multisymplectic manifold. We show that the existence/uniqueness theory governing these maps is a direct generalization from symplectic geometry.…

Homotopy comomentum maps are a higher generalization of the notion of moment map introduced to extend the concept of Hamiltonian actions to the framework of multisymplectic geometry. Loosely speaking, higher means passing from considering…

We introduce a notion of moment map adapted to actions of Lie groups that preserve a closed three-form. We show existence of our multi-moment maps in many circumstances, including mild topological assumptions on the underlying manifold.…

In this article a homotopy co-momentum map (\`a la Callies-Fr\'egier-Rogers-Zambon) trangressing to the standard hydrodynamical co-momentum map of Arnol'd, Marsden and Weinstein and others is constructed and then generalized to a special…

We introduce a notion of a homotopy momentum section on a Lie algebroid over a pre-multisymplectic manifold. A homotopy momentum section is a generalization of the momentum map with a Lie group action and the momentum section on a…

In this paper we show that the classical results on the existence and uniqueness of moment maps in symplectic geometry generalize directly to weak homotopy moment maps in multisym- plectic geometry. In particular, we show that their…

Given a complex balanced manifold $X$ and a compact complex manifold $S$ equipped with a positive volume form $dV>0$ and satisfying an extra condition such that $\mbox{dim}\,S\geq\mbox{dim}\,X -1$, we construct a moment map for the action…

We bring a linkage from representation theory of Lie groups to homotopy theory for maps between flag manifolds. As applications we derive from representation theory abundant families of homotopy classes of maps between flag manifolds whose…

moment maps arise as a generalization of genuine moment maps on symplectic manifolds when the symplectic structure is discarded, but the relation between the mapping and the action is kept. Particular examples of abstract moment maps had…

This Master Thesis is devoted to the study of $n$-plectic manifolds and the Strongly Homotopy Lie algebras, also called $L_{\infty}$-algebras, that can be associated to them. Since multisymplectic geometry and $L_{\infty}$-algebras are…

We investigate a notion of $\times$-homotopy of graph maps that is based on the internal hom associated to the categorical product in the category of graphs. It is shown that graph $\times$-homotopy is characterized by the topological…

While symplectic geometry is the geometric framework of classical mechanics, the geometry of classical field theories is governed by multisymplectic structures. In multisymplectic geometry, the Poisson algebra of Hamiltonian functions is…

The homotopy theory of representations of nets of algebras over a (small) category with values in a closed symmetric monoidal model category is developed. We illustrate how each morphism of nets of algebras determines a change-of-net…

We extend the definition of Weinstein's Action homomorphism to Hamiltonian actions with equivariant moment maps of (possibly infinite-dimensional) Lie groups on symplectic manifolds, and show that under conditions including a uniform bound…

We develop a theory of "quasi"-Hamiltonian G-spaces for which the moment map takes values in the group G itself rather than in the dual of the Lie algebra. The theory includes counterparts of Hamiltonian reductions, the Guillemin-Sternberg…

Normal maps between discrete groups $N\rightarrow G$ were characterized [FS] as those which induce a compatible topological group structure on the homotopy quotient $EN\times_N G$. Here we deal with topological group (or loop) maps…

We consider actions of reductive complex Lie groups $G=K^C$ on K\"ahler manifolds $X$ such that the $K$--action is Hamiltonian and prove then that the closures of the $G$--orbits are complex-analytic in $X$. This is used to characterize…