2 citations · 3 across the 5 of their papers we have counts for
5 papers
On singular foliations tangent to a given hypersurface
Michael Francis
We consider a class of singular foliations in the sense of Androulidakis and Skandalis that we call transverse order foliations. These have a finite number of leaves: one hyper…
H-Unitality of Smooth Groupoid Algebras
Michael Francis
We show that the convolution algebra of smooth, compactly-supported functions on a Lie groupoid is H-unital in the sense of Wodzicki. We also prove H-unitality of infinite order va…
The smooth algebra of a one-dimensional singular foliation
Michael Francis
Androulidakis and Skandalis showed how to associate a holonomy groupoid, a smooth convolution algebra and a C*-algebra to any singular foliation. In this note, we consider the sing…
A Dixmier-Malliavin theorem for Lie groupoids
Michael Francis
A famous theorem of Dixmier-Malliavin asserts that every smooth, compactly-supported function on a Lie group can be expressed as a finite sum in which each term is the convolution,…
Two Topological Uniqueness Theorems for Spaces of Real Numbers
Michael Francis
A 1910 theorem of Brouwer characterizes the Cantor set as the unique totally disconnected, compact metric space without isolated points. A 1920 theorem of Sierpinski characterizes…