On invariant linearization of Lie groupoids

Autor(es)

del Hoyo, Matias ^[1] ; de Melo, Mateus ^[2]

Afiliação do(s) autor(es)

^[1] Univ Fed Fluminense UFF, Rua Prof Marcos Waldemar Freitas Reis S-N, BR-24210201 Niteroi, RJ - Brazil

^[2] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: LETTERS IN MATHEMATICAL PHYSICS; v. 111, n. 4 AUG 2021.
• Citações Web of Science: 0

Resumo

The linearization theorem for proper Lie groupoids organizes and generalizes several results for classic geometries. Despite the various approaches and recent works on the subject, the problem of understanding invariant linearization remains somehow open. We address it here, by first giving a counter-example to a previous conjecture, and then proving a sufficient criterion that uses compatible complete metrics and covers the case of proper group actions. We also show a partial converse that fixes and extends previous results in the literature. (AU)

• Processo FAPESP: 19/14777-3 - As interações entre grupoides de Lie e Geometria Riemanniana
• Beneficiário: Mateus Moreira de Melo
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado