## 29 Citations

Geometric Complexity Theory -- Lie Algebraic Methods for Projective Limits of Stable Points

- Mathematics
- 2022

The primary objective is to understand the points [y], and their stabilizers, which occur in the vicinity of [x] in PV, and an explicit Lie algebra action of G is constructed on a suitably parametrized neighbourhood of x, showing that the Lie algebras of the stabilizers of points in the neighbourhood ofx are parameterized by subspaces of H.

The Infinitesimalization and Reconstruction of Locally Homogeneous Manifolds

- Mathematics
- 2013

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 con- nected manifold M is locally…

Completing Lie algebra actions to Lie group actions

- Mathematics
- 2003

For a finite dimensional Lie algebra $\g$ of vector fields on a manifold $M$ we show that $M$ can be completed to a $G$-space in a unversal way, which however is neither Hausdorff nor $T_1$ in…

Cohomology of Horizontal Forms

- Mathematics
- 2012

The complex of s-horizontal forms of a smooth foliation F on a manifold M is proved to be exact for every s = 1, . . . , n = codim F, and the cohomology groups of the complex of its global sections,…

Singular Poisson Reduction of Cotangent Bundles

- Mathematics
- 2005

We consider the Poisson reduced space (T Q)/K , where the action of the com pact Lie group K on the configuration manifold Q is of single orbit type and is cotangent lifted to T Q. Realizing (T Q)/K…

A cotangent bundle Hamiltonian tube theorem and its applications in reduction theory

- Mathematics
- 2015

The Marle-Guillemin-Sternberg (MGS) model is an extremely important tool for the theory of Hamiltonian actions on symplectic manifolds. It has been extensively used to prove many local results both…

Geometric foundations of Cartan gauge gravity

- Physics
- 2015

We use the theory of Cartan connections to analyze the geometrical structures underpinning the gauge-theoretical descriptions of the gravitational interaction. According to the theory of Cartan…

On Heisenberg normal structures

- Mathematics
- 2016

We consider higher dimensional generalisations of normal almost contact structures. Two types of these structures are discussed. In the first case we replace an action of $\mathbb{R}$ (which is the…

Local reflexion spaces

- Mathematics
- 2012

A reflexion space is generalization of a symmetric space introduced by O. Loos in [6]. We generalize locally symmetric spaces to local reflexion spaces in the similar way. We investigate, when local…

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- Mathematics
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- Mathematics
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