| Texto completo | |
| Autor(es): |
Ortiz, Cristian
;
Valencia, Fabricio
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | MATHEMATISCHE ZEITSCHRIFT; v. 307, n. 3, p. 55-pg., 2024-07-01. |
| Resumo | |
In this paper we introduce Morse Lie groupoid morphisms and study their main properties. We show that this notion is Morita invariant which gives rise to a well defined notion of Morse function on differentiable stacks. We show a groupoid version of the Morse lemma which is used to describe the topological behavior of the critical subgroupoid levels of a Morse Lie groupoid morphism around its nondegenerate critical orbits. We also prove Morse type inequalities for certain separated differentiable stacks and construct a Morse double complex whose total cohomology is isomorphic to the Bott-Shulman-Stasheff cohomology of the underlying Lie groupoid. We provide several examples and applications. (AU) | |
| Processo FAPESP: | 22/11994-6 - Geodésicas fechadas em stacks Riemannianos |
| Beneficiário: | Fabricio Valencia Quintero |
| Modalidade de apoio: | Bolsas no Exterior - Estágio de Pesquisa - Doutorado |
| 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 |
| Processo FAPESP: | 22/09234-3 - Ações Hamiltonianas em stacks, cohomologia equivariante e localização |
| Beneficiário: | Cristián Andrés Ortiz González |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |