Maslov-Type Index Theory for Symplectic Paths and Spectral Flow (II)

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 ω-index theory parameterized by all ω 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 / 58E05 / 58G99 / O176.3 / O19

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