Symplectic dynamics and spectral sequences

• Grant number: 15/10930-0
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Effective date (Start): September 01, 2015
• Effective date (End): August 31, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Ketty Abaroa de Rezende
• Grantee: Dahisy Valadão de Souza Lima
• Supervisor: Eric Zaslow
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Research place: Northwestern University, Evanston, United States
• Associated to the scholarship: 14/11943-6 - Spectral sequences for Morse-Bott and Morse-Novikov flows study, BP.PD

Abstract

Morse theory features very prominently in modern mathematical physics, specifically the Fukaya category of Lagrangian submanifolds of a symplectic manifold, and in the theory of generating functions of Legendrian submanifolds of a first jet bundle. These two examples have overlap: the Lagrangian conormal of a knot in three-space defines a Legendrian submanifold of the contact unit cosphere bundle. Fukaya and Oh formulated this study in the context of Morse Theory. Our goal will be to study the invariance of generating families of Morse functions which are associated to Legendrian invariants through continuation maps defined in the Conley Index Theory as well as the use of techniques involving connection matrices and spectral sequences of Morse complexes in order to determine birth and death of connections through handle moves. (AU)

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)

LIMA, D. V. S.; RAMINELLI, S. A.; DE REZENDE, K. A.. HOMOTOPICAL CANCELLATION THEORY FOR GUTIERREZ-SOTOMAYOR SINGULAR FLOWS. JOURNAL OF SINGULARITIES, v. 23, p. 33-91, 2021. (14/11943-6, 18/13481-0, 15/10930-0, 16/24707-4)

LIMA, DAHISY V. DE S.; MANZOLI NETO, OZIRIDE; DE REZENDE, KETTY A.; DA SILVEIRA, MARIANA R.. CANCELLATIONS FOR CIRCLE-VALUED MORSE FUNCTIONS VIA SPECTRAL SEQUENCES. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, v. 51, n. 1, p. 259-311, MAR 2018. (15/10930-0, 12/18780-0, 14/11943-6)