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Continuous Hamiltonian dynamics and area-preserving homeomorphism group of D2

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Title
Continuous Hamiltonian dynamics and area-preserving homeomorphism group of D2
Author(s)
Yong-Geun Oh
Publication Date
2016-07
Journal
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, v.53, no.4, pp.195 - 834
Publisher
KOREAN MATHEMATICAL SOC
Abstract
The main purpose of this paper is to propose a scheme of a proof of the nonsimpleness of the group HomeoΩ(D2 , ∂D2 ) of area pre- serving homeomorphisms of the 2-disc D2. We first establish the exis- tence of Alexander isotopy in the category of Hamiltonian homeomor- phisms. This reduces the question of extendability of the well-known Calabi homomorphism Cal : DiffΩ(D1 , ∂D2) → R to a homomorphism Cal : Hameo(D2 , ∂D2 ) → R to that of the vanishing of the basic phase function fF, a Floer theoretic graph selector constructed in [9], that is associated to the graph of the topological Hamiltonian loop and its nor- malized Hamiltonian F on S2 that is obtained via the natural embedding D2 ֒→ S2. Here Hameo(D2, ∂D2 ) is the group of Hamiltonian homeo- morphisms introduced by Mu¨ller and the author [18]. We then provide an evidence of this vanishing conjecture by proving the conjecture for the special class of weakly graphical topological Hamiltonian loops on D2 via the associated Hamiton-Jacobi equation. c 2016 Korean Mathematical Society
URI
https://pr.ibs.re.kr/handle/8788114/2716
ISSN
0304-9914
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > Journal Papers (저널논문)
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