Approximation of Generating Function Barcode for Hamiltonian Diffeomorphisms

Abstract: Persistence modules and barcodes are used in symplectic topology to define new invariants of Hamiltonian diffeomorphisms, however methods that explicitly calculate these barcodes are often unclear. In this talk I will explain the necessary background and define one such invariant called the GF-barcode of compactly supported Hamiltonian diffeomorphisms of $ \mathbb{R}^{2n} $ by applying Morse theory to generating functions quadratic at infinity associated to such Hamiltonian diffeomorphisms and provide an algorithm (i.e a finite sequence of explicit calculation steps) that approximates it along with a few computation examples. Joint work with Pazit Haim-Kislev.

differential geometrydynamical systemsgeometric topologysymplectic geometry

Audience: researchers in the topic

Geometry and Dynamics seminar

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