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| MASLOV-TYPE INDEX THEORY FOR SYMPLECTIC PATHS AND SPECTRAL FLOW(II) |
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Citation： |
LONG Yiming.MASLOV-TYPE INDEX THEORY FOR SYMPLECTIC PATHS AND SPECTRAL FLOW(II)[J].Chinese Annals of Mathematics B,2000,21(1):89~108 |
| Page view： 1682
Net amount： 1016 |
Authors： |
LONG Yiming; |
Foundation： |
Project supported by the National Natural Science Foundation of China and MCSEC of China and the Qiu Shi Science and Technology Foundation. |
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| Abstract： |
Based on the spectral flow and the stratification structures of the symplectic group $\Sp(2n,\C)$, the Maslov-type index theory and its generalization, the $\om$-index theory parameterized by all $\om$ on the unit circle, for arbitrary paths in
$\Sp(2n,\C)$ are established. Then the Bott-type iteration formula of the Maslov-type indices for iterated paths in $\Sp(2n,\C)$ is proved, and the mean index for any path in $\Sp(2n,\C)$ is defined. Also, the relation among various Maslov-type index theories is studied. |
Keywords： |
Maslov-type index theory, Symplectic path, Spectral flow, Relative Morse index, ω-index |
Classification： |
58E05, 58G99 |
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