Director of Research (if dissertation) or Advisor (if thesis)
Loja Fernandes, Rui A
Doctoral Committee Chair(s)
Kerman, Ely
Committee Member(s)
Pascaleff, James
Berwick Evans, Daniel
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
abelianization
Lie algebroid
groupoid
diffeology
genus-integration
Abstract
This thesis discusses abelianization of Lie algebroids and groupoids in different categories. In Chapter 2 we find a sufficient and necessary condition for a Lie algebroid to admit an abelianization and give several examps and applications. In Chapter 3 we prove that every (locally subductive) diffeological groupoid has a (locally subductive) abelianization. We also find a sufficient condition for a Lie groupoid to admit a smooth abelianization and study the smoothness of the genus-integration, the set-theoretical abelianization of the Weinstein groupoid.
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