3-2-1 foliations for Reeb flows on S³

Author(s)

Carolina Lemos de Oliveira

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI)
• Defense date: 2020-03-06

Examining board members

Pedro Antonio Santoro Salomão; Naiara Vergian de Paulo Costa; Umberto Leone Hryniewicz; Alexsandro Schneider; André Vanderlinde da Silva

• Advisor: Pedro Antonio Santoro Salomão

Abstract

In this work, we study global systems of transverse sections for Reeb flows associated with tight contact forms on the 3-sphere. These flows include, in particular, Hamiltonian flows on R^4 restricted to star-shaped regular energy levels. A global system of transverse sections naturally generalizes the concept of global surface of section. It is a singular foliation of S³ whose singular set consists of finitely many periodic orbits, called binding orbits, and the regular leaves are transverse to the flow. The aim of this work is to use the theory of pseudoholomorphic curves in symplectizations to study the existence of a particular type of system of transverse sections, called 3-2-1 foliation, which has exactly three binding orbits with Conley-Zehnder indices respectively 3, 2 and 1. More precisely, we give sufficient conditions under which three Reeb orbits are the binding orbits of a 3-2-1 foliation. (AU)

• FAPESP's process: 16/10466-5 - Reeb flows and finite energy foliations
• Grantee: Carolina Lemos de Oliveira
• Support Opportunities: Scholarships in Brazil - Doctorate