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Generalized Symplectic Action and Symplectomorphism Groups of Coadjoint Orbits

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An Erratum to this article was published on 18 July 2008

Abstract

Let M be a quantizable symplectic manifold. If ψ t is a loop in the group {Ham}(M) of Hamiltonian symplectomorphisms of M and A is a 2k-cycle in M, we define a symplectic action κ A (ψ)∊ U(1) around ψ t (A), which is invariant under deformations of ψ, and such that κ A (ψ) depends only on the homology class of A. Using properties of κ A ( ) we determine a lower bound for ♯π1(Ham(O)), where O is a quantizable coadjoint orbit of a compact Lie group. In particular we prove that ♯π1(Ham(C P n)) ≥ n+1.

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Authors and Affiliations

  1. Departamento de Física, Universidad de Oviedo, Avda Calvo Sotelo, 33007, Oviedo, Spain

    Andrés Viña

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  1. Andrés Viña
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Correspondence to Andrés Viña.

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Mathematics Subject Classifications (2000): 53D05, 57S05, 57R17, 57T20.

An erratum to this article is available at http://dx.doi.org/10.1007/s10455-008-9117-9.

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Viña, A. Generalized Symplectic Action and Symplectomorphism Groups of Coadjoint Orbits. Ann Glob Anal Geom 28, 309–318 (2005). https://doi.org/10.1007/s10455-005-1150-3

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  • DOI: https://doi.org/10.1007/s10455-005-1150-3

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