Spectral invariants, analysis of the Floer moduli spaces and geometry of the Hamiltonian diffeomorphism group

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dc.creatorOh, Yong-Geun
dc.date2004-03-03
dc.date2005-02-19
dc.date.accessioned2026-07-07T06:24:40Z
dc.date.available2026-07-07T06:24:40Z
dc.descriptionIn this paper, we apply spectral invariants, constructed in [Oh5,8], to the study of Hamiltonian diffeomorphisms of closed symplectic manifolds $(M,ω)$. Using spectral invariants, we first construct an invariant norm called the {\it spectral norm} on the Hamiltonian diffeomorphism group and obtain several lower bounds for the spectral norm in terms of the $\e$-regularity theorem and the symplectic area of certain pseudo-holomorphic curves. We then apply spectral invariants to the study of length minimizing properties of certain Hamiltonian paths {\it among all paths}. In addition to the construction of spectral invariants, these applications rely heavily on the {\it chain level Floer theory} and on some existence theorems with energy bounds of pseudo-holomorphic sections of certain Hamiltonian fibrations with prescribed monodromy. The existence scheme that we develop in this paper in turn relies on some careful geometric analysis involving {\it adiabatic degeneration} and {\it thick-thin decomposition} of the Floer moduli spaces which has an independent interest of its own. We assume that $(M,ω)$ is {\it strongly semi-positive} throughout, which will be removed in a sequel.
dc.description78 pages, This the final version that will appear in Duke Math. J. published by Duke University Press
dc.identifierhttps://arxiv.org/abs/math/0403083
dc.identifierhttp://arxiv.org/abs/math/0403083
dc.identifierDuke Math. J. 130 (2005) , no2, 199-295
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/96622
dc.subjectSymplectic Geometry
dc.subject53D35, 53D40
dc.titleSpectral invariants, analysis of the Floer moduli spaces and geometry of the Hamiltonian diffeomorphism group
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