| Full text | |
| Author(s): |
Herrera-Carmona, Juan Sebastian
;
Valencia, Fabricio
Total Authors: 2
|
| Document type: | Journal article |
| Source: | JOURNAL OF GEOMETRIC ANALYSIS; v. 33, n. 10, p. 36-pg., 2023-10-01. |
| 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. (AU) | |
| FAPESP's process: | 20/07704-7 - Morse theory on Lie groupoids and stacks |
| Grantee: | Fabricio Valencia Quintero |
| Support Opportunities: | Scholarships in Brazil - Doctorate |