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Inertia Groupoids and their singularity structure or why we need a concept of stratified groupoids

Banff International Research Station for Mathematical Innovation and Discovery

The inertia space of a compact Lie group action or more generally of a proper Lie groupoid has an interesting singularity structure. Unlike the quotient space of the group action, respectively the groupoid, the inertia space can not be stratified by orbit types, in general. In the talk we explain this phenomenon and provide a stratification and local description of the inertia space. Moreover, we show that that leads naturally to the concept of a stratified groupoid which lies in between the one of a Lie groupoid and the one of a topological groupoid. Finally we show that a de Rham theorem holds for inertia spaces and explain the connection of the inertia space with the non-commutative geometry of the underlying groupoid.

Mathematics; Differential geometry; Topological groups, lie groups

video/mp4

Author affiliation: University of Colorado Boulder

2017-10-18

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63335

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/