67 citations · 104 across the 15 of their papers we have counts for
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Lie Algebroid Invariants for Subgeometry
Anthony D. Blaom
We investigate the infinitesimal invariants of an immersed submanifold of a Klein geometry , and in particular an invariant filtration of Lie algebroids over . T…
The Lie algebroid associated with a hypersurface
Anthony D. Blaom
In this note we motivate the definition and use of Lie algebroids by revisiting the problem of reconstructing a hypersurface in Euclidean space from infinitesimal data.
A Characterisation of Smooth Maps into a Homogeneous Space
Anthony D. Blaom
We generalize Cartan's logarithmic derivative of a smooth map from a manifold into a Lie group to smooth maps into a homogeneous space , and determine the global monodro…
Cartan Connections on Lie Groupoids and their Integrability
Anthony D. Blaom
A multiplicatively closed, horizontal -plane field on a Lie groupoid over generalizes to intransitive geometry the classical notion of a Cartan connection. The infin…
Pseudogroups via pseudoactions: Unifying local, global, and infinitesimal symmetry
Anthony D. Blaom
A multiplicatively closed, horizontal foliation on a Lie groupoid may be viewed as a "pseudoaction" on the base manifold . A pseudoaction generates a pseudogroup of transformati…
The Infinitesimalization and Reconstruction of Locally Homogeneous Manifolds
Anthony D. Blaom
A linear connection on a Lie algebroid is called a Cartan connection if it is suitably compatible with the Lie algebroid structure. Here we show that a smooth connected manifold $M…
Lie algebroids and Cartan's method of equivalence
Anthony D. Blaom
Elie Cartan's general equivalence problem is recast in the language of Lie algebroids. The resulting formalism, being coordinate and model-free, allows for a full geometric interpr…
Geometric structures as deformed infinitesimal symmetries
Anthony D. Blaom
A general model for geometric structures on differentiable manifolds is obtained by deforming infinitesimal symmetries. Specifically, this model consists of a Lie algebroid, equipp…