The Maslov index for paths
type: Item
instance of: scholarly article
title: The Maslov index for paths
zbMATH Open document ID: 0798.58018
DOI: 10.1016/0040-9383(93)90052-W
published in: Topology
publication date: 1994-11-03T00:00:00Z
review text: In Funct. Anal. Appl. 1, No. 1, 1-13 (1967); translation from Funkts. Anal. Prilozh. 1, No. 1, 1-14 (1967; Zbl 0175.203) \textit{V. I. Arnol'd} interpreted the Maslov index for a loop of Lagrangian subspaces as an interaction number with an algebraic variety known as the Maslov cycle. Arnol'd's general position arguments apply equally well to the case of a path of Lagrangian subspaces whose endpoints lie in the complement of the Maslov cycle. In this paper the authors define a Maslov index for any continuous path of Lagrangian subspaces. This index depends on the choice of the Lagrangian subspace used to define the Maslov cycle, is invariant under homotopy with fixed endpoints and is additive for catenations. Moreover the authors use the above index to define a Maslov index for paths of symplectic matrices. This latter index is characterized axiomatically and it leads to a stratification of the symplectic group \(\text{Sp}(2n)\).
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 550345
zbMATH Keywords: Lagrangian path
zbMATH Keywords: Maslov index
zbMATH Keywords: Maslov cycle
zbMATH Keywords: symplectic matrices
author: Joel W. Robbin
author: Dietmar A. Salamon
reviewed by: Enrique Outerelo
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 550345