Geodesic
L'Indice de Maslov en Dimension Infinie
Journal of Lie theory, Tome 18 (2008) no. 1, pp. 161-18
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Let E be a JB*-triple whose set of invertible tripotents Σ is not empty. We construct a homotopy invariant index for paths in Σ that satisfy a Fredholm type condition with respect to a fixed invertible tripotent. This index generalises the Maslov index for the Fredholm-Lagrangian of an infinite dimensional symplectic Hilbert space as defined by B. Booss-Bavnbek and K. Furutani ["The Maslov index: a functional analytical definition and the spectral flow formula", Tokyo Journal of Mathematics 21 (1998) 1--34]. When E is finite dimensional we make the connection with the generalised triple index of J.-L. Clerc and B. Oersted ["The Maslov index revisited", Transformation Groups 6 (2001) 303--320], and of J.-L. Clerc ["L'indice de Maslov généralisé, Journal de Mathématiques Pures et Appliquées, Neuvième Série 83 (2004) 99--114], and with the generalised Souriau index of J.-L. Clerc and K. Koufany ["Primitive du cocycle de Maslov généralisé, Mathematische Annalen 337 (2007) 91--138].
Classification : 53D12, 17C65, 32M15
Mots-clés : Maslov index, bounded symmetric domains, Banach-Jordan algebras 
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     author = {S. Merigon},
     title = {L'Indice de {Maslov} en {Dimension} {Infinie}},
     journal = {Journal of Lie theory},
     pages = {161--18},
     year = {2008},
     volume = {18},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JLT_2008_18_1_JLT_2008_18_1_a9/}
}
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S. Merigon. L'Indice de Maslov en Dimension Infinie. Journal of Lie theory, Tome 18 (2008) no. 1, pp. 161-18. http://geodesic.mathdoc.fr/item/JLT_2008_18_1_JLT_2008_18_1_a9/