Constructs automorphism 2-group of Lie groupoids, equates homomorphisms to Kan fibrations, and shows symplectic reductions under étale Lie 2-group Hamiltonian actions yield symplectic Lie 2-groupoids or orbifolds under isotropic free conditions, plus a slice theorem.
Higher Groupoid Actions, Bibundles, and Differentiation
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abstract
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.
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2026 1verdicts
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Automorphisms of Lie groupoids and symplectic reduction on orbifolds
Constructs automorphism 2-group of Lie groupoids, equates homomorphisms to Kan fibrations, and shows symplectic reductions under étale Lie 2-group Hamiltonian actions yield symplectic Lie 2-groupoids or orbifolds under isotropic free conditions, plus a slice theorem.