Groupoids and Algebras of Certain Singular Foliations with Finitely Many Leaves
Open Access
Author:
Francis, Michael
Graduate Program:
Mathematics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
June 10, 2021
Committee Members:
Ping Xu, Major Field Member Nigel Higson, Chair & Dissertation Advisor Martin Bojowald, Outside Unit & Field Member Nathanial Brown, Major Field Member Alexei Novikov, Program Head/Chair
Given any singular foliation, Androulidakis and Skandalis showed how to construct a holonomy groupoid, a smooth convolution algebra and a C*-algebra. In this thesis, we study certain classes of singular foliations which have only finitely many leaves. The main results take the form of classifications of these foliations and descriptions of their groupoids and algebras. Along the way, we prove a Lie groupoid analog of a theorem of Dixmier and Malliavin.
