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Go Fishing with Alice: Compatible Carrollian and Poisson Structures
Andrew James Bruce
We introduce, motivated by noncommutative Carrollian geometry, the notion of a Carrollian--Poisson bundle understood as a Carrollian manifold with a compatible Poisson structure. C…
Carrollian Lie Algebroids: Taming Singular Carrollian Geometries
Andrew James Bruce
Developments in Carrollian gravity and holography necessitate the use of singular Carroll vector fields, a feature that cannot be accommodated within standard Carrollian geometry.…
On a Grassmann odd analogue of Carrollian Manifolds
Andrew James Bruce
We define a Grassmann odd analogue of a Carrollian manifold as a supermanifold of dimension with an even degenerate metric such that the kernel is generated by a non-singular…
Carrollian -bundles III: The Hodge Star and Hodge--de Rham Laplacians
Andrew James Bruce
Carrollian -bundles () offer a novel perspective on intrinsic Carrollian geometry using the powerful tools of pri…
Carrollian -bundles: Connections and Beyond
Andrew James Bruce
We propose an approach to Carrollian geometry using principal -bundles ($\mathbb{R}^\times := \matthbb{R} \setminus \{0\}$) equipped with a degenerate metric who…