Isometric Lie 2-Group Actions on Riemannian Groupoids

Autor(es)

Herrera-Carmona, Juan Sebastian ; Valencia, Fabricio

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF GEOMETRIC ANALYSIS; v. 33, n. 10, p. 36-pg., 2023-10-01.

Resumo

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. (AU)

• Processo FAPESP: 20/07704-7 - Teoria de Morse em grupoides de Lie e stacks
• Beneficiário: Fabricio Valencia Quintero
• Modalidade de apoio: Bolsas no Brasil - Doutorado