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The Lie Group Structure of the Butcher Group
TLDR
The Butcher group is complemented with a natural infinite-dimensional Lie group structure that turns the Butcher group into a real analytic Baker–Campbell–Hausdorff Lie group modelled on a Fréchet space.
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Extending Whitney’s extension theorem: nonlinear function spaces
This article shows that there is a continuous extension operator for compactly-supported smooth sections of vector bundles on possibly non-compact smooth manifolds, where the closed set to which…
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The Lie group of bisections of a Lie groupoid
In this article, we endow the group of bisections of a Lie groupoid with compact base with a natural locally convex Lie group structure. Moreover, we develop thoroughly the connection to the algebra…
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Shape analysis on homogeneous spaces
Shape analysis is ubiquitous in problems of pattern and object recognition and has developed considerably in the last decade. The use of shapes is natural in applications where one wants to compare…
Shape Analysis on Homogeneous Spaces: A Generalised SRVT Framework
Shape analysis is ubiquitous in problems of pattern and object recognition and has developed considerably in the last decade. The use of shapes is natural in applications where one wants to compare…
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Manifolds of absolutely continuous curves and the square root velocity framework
A classical result in Riemannian geometry states that the absolutely continuous curves into a (finite-dimensional) Riemannian manifold form an infinite-dimensional manifold. In the present paper this…
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Lie groupoids of mappings taking values in a Lie groupoid
Endowing differentiable functions from a compact manifold to a Lie group with the pointwise group operations one obtains the so-called current groups and, as a special case, loop groups. These are…
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The Lie group of real analytic diffeomorphisms is not real analytic
We construct an infinite dimensional real analytic manifold structure for the space of real analytic mappings from a compact manifold to a locally convex manifold. Here a map is real analytic if it…
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Differentiable mappings on products with different degrees of differentiability in the two factors
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The tame Butcher group
The Butcher group is a powerful tool to analyse integration methods for ordinary differential equations, in particular Runge--Kutta methods. Recently, a natural Lie group structure has been…
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