Morse theory on Lie groupoids and stacks

• Grant number: 20/07704-7
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: December 01, 2020
• End date: October 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Cristián Andrés Ortiz González
• Grantee: Fabricio Valencia Quintero
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated scholarship(s): 22/11994-6 - Closed geodesics on Riemannian stacks, BE.EP.DR

Abstract

In this project we propose a generalization of classical Morse theory to the setting of Lie groupoids. This offers a unified approach to study equivariant Morse theory and Morse theory on orbifolds. As applications, we will investigate the existence of closed geodesics on Riemannian stacks and cohomological properties of symplectic reductions of Hamiltonian Lie 2-group actions on étale symplectic groupoids.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

VALENCIA, FABRICIO; VAREA, CARLOS. Invariant Generalized Almost Complex Structures on Real Flag Manifolds. JOURNAL OF GEOMETRIC ANALYSIS, v. 32, n. 12, p. 40-pg., 2022-12-01. (20/07704-7, 20/12018-5)

HERRERA-CARMONA, JUAN SEBASTIAN; VALENCIA, FABRICIO. Isometric Lie 2-Group Actions on Riemannian Groupoids. JOURNAL OF GEOMETRIC ANALYSIS, v. 33, n. 10, p. 36-pg., 2023-10-01. (20/07704-7)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

QUINTERO, Fabricio Valencia. Morse theory on Lie groupoids. 2024. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.