Normalization of the Hamiltonian and the action spectrum

2002/06/26 by Yong-Geun Oh · 1 citation
Mathematics · #math.SG #math.DG #msc:53D35 #msc:53D05

paper · pdf

published as J. Korean Math. Soc. 42 (2005), No. 1, 65 - 83 · 15 pages, typos corrected

arxiv created 2002/06/26 · arxiv updated 2009/11/30

Abstract

In this paper, we prove that the two well-known natural normalizations of Hamiltonian functions on the symplectic manifold (M,ω) canonically relates the action spectra of different normalized Hamiltonians on \it arbitrary symplectic manifolds (M,ω). The natural class of normalized Hamiltonians consists of those whose mean value is zero for the closed manifold, and those which are compactly supported in Int M for the open manifold. We also study the effect of the action spectrum under the π₁ of Hamiltonian diffeomorphism group. This forms a foundational basis for our study of spectral invariants of the Hamiltonian diffeomorphism in [Oh4].

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• Smooth perfectness of Hamiltonian diffeomorphism groups

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