Construction of spectral invariants of Hamiltonian paths on closed symplectic manifolds
Abstrak
In this paper, we develop a mini-max theory of the action functional over the semi-infinite cycles via the chain level Floer homology theory and construct spectral invariants of Hamiltonian diffeomorphisms on arbitrary, especially on {\it non-exact and non-rational}, compact symplectic manifold $(M,ω)$. To each given time dependent Hamiltonian function $H$ and quantum cohomology class $ 0 \neq a \in QH^*(M)$, we associate an invariant $ρ(H;a)$ which varies continuously over $H$ in the $C^0$-topology. This is obtained as the mini-max value over the semi-infinite cycles whose homology class is `dual' to the given quantum cohomology class $a$ on the covering space $\widetilde Ω_0(M)$ of the contractible loop space $Ω_0(M)$. We call them the {\it Novikov Floer cycles}. We apply the spectral invariants to the study of Hamiltonian diffeomorphisms in sequels of this paper.
Topik & Kata Kunci
Penulis (1)
Yong-Geun Oh
Akses Cepat
- Tahun Terbit
- 2004
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓