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Symplectic dynamics and spectral sequences

Grant number: 15/10930-0
Support type: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 researcher:Ketty Abaroa de Rezende
Grantee:Dahisy Valadão de Souza Lima
Supervisor abroad: Eric Zaslow
Home 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)

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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, 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, . (15/10930-0, 12/18780-0, 14/11943-6)
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, . (14/11943-6, 18/13481-0, 15/10930-0, 16/24707-4)

Please report errors in scientific publications list by writing to: cdi@fapesp.br.