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- W4296544629 abstract "We study isometric actions of Lie $2$-groups on Riemannian groupoids by exhibiting some of their immediate properties and implications. Firstly, we prove an existence result which allows both to obtain 2-equivariant versions of the Slice Theorem and the Equivariant Tubular Neighborhood Theorem and to construct bi-invariant groupoid metrics on compact Lie $2$-groups. We provide natural examples, transfer some classical constructions and explain how this notion of isometric $2$-action yields a way to develop a 2-equivariant Morse theory on Lie groupoids. Secondly, we give an infinitesimal description of an isometric Lie $2$-group action. We define an algebra of transversal infinitesimal isometries associated to any Riemannian $n$-metric on a Lie groupoid which in turn gives rise to a notion of geometric Killing vector field on a quotient Riemannian stack. If our Riemannian stack is separated then we prove that the algebra formed by such geometric Killing vector fields is always finite dimensional." @default.
- W4296544629 created "2022-09-21" @default.
- W4296544629 creator A5059758738 @default.
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- W4296544629 date "2022-09-18" @default.
- W4296544629 modified "2023-09-28" @default.
- W4296544629 title "Isometric Lie 2-group actions on Riemannian groupoids" @default.
- W4296544629 doi "https://doi.org/10.48550/arxiv.2209.08643" @default.
- W4296544629 hasPublicationYear "2022" @default.
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