35 citations · 97 across the 13 of their papers we have counts for
14 papers
Actions of Lie 2-algebras and comomentum maps
Philippe Bonneau, Véronique Chloup-Arnould, Angela Gammella +1
In this paper we introduce the notion of a 2-action of a Lie 2-algebra on an arbitrary manifold M. Furthermore, in [Rog12], given a n-plectic manifold (M, ), the authors conside…
Hamiltonian dynamics and geometry on the two-plectic six-sphere
Maxime Wagner, Tilmann Wurzbacher
We study the two-plectic geometry of the six-sphere induced by pulling back a canonical -invariant three-form from . Notably we explicitly prove non-flatness of…
Notes on equivalent formulations of Hamiltonian dynamics on multicotangent bundles
Maxime Wagner, Tilmann Wurzbacher
We show the equivalence of five different conditions on a classical field with values in a restricted multicotangent bundle to be a solution of the field equations, notably in…
On the prequantisation map for 2-plectic manifolds
Gabriel Sevestre, Tilmann Wurzbacher
For a manifold with an integral closed 3-form , we construct a -bundle and a Lie groupoid over its total space, together with a curving in the sense of gerbes. If the…
Lagrangian submanifolds of standard multisymplectic manifolds
Gabriel Sevestre, Tilmann Wurzbacher
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…
An invitation to multisymplectic geometry
Leonid Ryvkin, Tilmann Wurzbacher
In this article we study multisymplectic geometry, i.e., the geometry of manifolds with a non-degenerate, closed differential form. First we describe the transition from Lagrangian…
Conserved quantities on multisymplectic manifolds
Leonid Ryvkin, Tilmann Wurzbacher, Marco Zambon
Given a vector field on a manifold M, we define a globally conserved quantity to be a differential form whose Lie derivative is exact. Integrals of conserved quantities over suitab…
Superorbits
Alexander Alldridge, Joachim Hilgert, Tilmann Wurzbacher
We study actions of Lie supergroups, in particular, the hitherto elusive notion of orbits through odd (or more general) points. Following categorical principles, we derive a concep…
Existence and unicity of co-moments in multisymplectic geometry
Leonid Ryvkin, Tilmann Wurzbacher
Given a multisymplectic manifold and a Lie algebra acting on it by infinitesimal symmetries, Fregier-Rogers-Zambon define a homotopy (co-)moment as an $L_{\infty…
Infinite-dimensional manifolds as ringed spaces
Michel Egeileh, Tilmann Wurzbacher
We analyze the possibility of defining infinite-dimensional manifolds as ringed spaces. More precisely, we consider three definitions of manifolds modeled on locally convex spaces:…
Singular superspaces
Alexander Alldridge, Joachim Hilgert, Tilmann Wurzbacher
We introduce a wide category of superspaces, called locally finitely generated, which properly includes supermanifolds but enjoys much stronger permanence properties, as are prompt…
Integration of vector fields on smooth and holomorphic supermanifolds
Stéphane Garnier, Tilmann Wurzbacher
We give a new and self-contained proof of the existence and unicity of the flow for an arbitrary (not necessarily homogeneous) smooth vector field on a real supermanifold, and exte…
The geodesic flow on a Riemannian supermanifold
Stéphane Garnier, Tilmann Wurzbacher
We give a natural definition of geodesics on a Riemannian supermanifold and extend the usual geodesic flow defined on the cotangent bundle of the body of the supermanifold, associa…
On the geometry and quantization of symplectic Howe pairs
Carsten Balleier, Tilmann Wurzbacher
We study the orbit structure and the geometric quantization of a pair of mutually commuting hamiltonian actions on a symplectic manifold. If the pair of actions fulfils a symplecti…