Abstract
In this note, the relations between various index theories are established. For example, the relationship between the Maslov type index for symplectic paths, the P-index for symplectic paths, L-index for symplectic paths, and the index theory for paths of Lagrangian subspaces is considered. To study the difference between two index theories, we introduce the Hörmander index theory for four lagrangian subspaces and show that all the differences between two indices are exactly the Hörmander index for suitable four Lagrangian subspaces.
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Dedicated to Professor Paul H. Rabinowitz.
C. Liu is partially supported by the NSF of China (11471170, 10621101), 973 Program of MOST (2011CB808002) and SRFDP.
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Liu, C. A note on the relations between the various index theories. J. Fixed Point Theory Appl. 19, 617–648 (2017). https://doi.org/10.1007/s11784-016-0368-y
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DOI: https://doi.org/10.1007/s11784-016-0368-y