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

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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 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.

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Authors and Affiliations

  1. Nankai Institute of Mathematics, Nankai University, Tianjin, 300071, China

    Yiming Long & Chaofeng Zhu

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  1. Yiming Long
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  2. Chaofeng Zhu
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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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Long, Y., Zhu, C. Maslov-Type Index Theory for Symplectic Paths and Spectral Flow (II). Chin. Ann. of Math. 21, 89–108 (2000). https://doi.org/10.1007/BF02731963

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  • DOI: https://doi.org/10.1007/BF02731963

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