Higher Groupoid Actions, Bibundles, and Differentiation

by Du Li
Doctoral thesis
Date of Examination:2014-07-15
Date of issue:2014-08-13
Advisor:Prof. Dr. Chenchang Zhu
Referee:Prof. Dr. Chenchang Zhu
Referee:Prof. Dr. Ralf Meyer
Persistent Address: http://dx.doi.org/10.53846/goediss-4622

 

 

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Abstract

English

In this thesis, we employ simplicial methods to study actions, principal bundles and bibundles of higher groupoids. Roughly, we use Kan fibrations to model actions of higher groupoids; we use pairs of a Kan fibration and a special acyclic fibration to model principal bundles of higher groupoids; we use inner Kan fibrations over the interval to model bibundles of higher groupoids. In particular, we show that our definitions given by the simplicial method agree with those given by the categorification approach to actions, principal bundles, and bibundles of 2-groupoids.     In addition, we use the simplicial technique to prove a theorem on differentiation of higher Lie groupoids, which shows that the differentiation functor sends a higher Lie groupoid to a higher Lie algebroid.
Keywords: higher groupoids; higher Lie groupoids; higher groupoid actions; higher groupoid bibundles; differentiation of higher Lie groupoids
 
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