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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 10th 2013

    Added to Maslov index and to Lagrangian Grassmannian the following quick cohomological definition of the Maslov index:

    The first ordinary cohomology of the stable Lagrangian Grassmannian with integer coefficients is isomorphic to the integers

    H 1(LGrass,). H^1(LGrass, \mathbb{Z}) \simeq \mathbb{Z} \,.

    The generator of this cohomology group is called the universal Maslov index

    uH 1(LGrass,). u \in H^1(LGrass, \mathbb{Z}) \,.

    Given a Lagrangian submanifold YXY \hookrightarrow X of a symplectic manifold (X,ω)(X,\omega), its tangent bundle is classified by a function

    i:YLGrass. i \;\colon\; Y \to LGrass \,.

    The _Maslov index of YY is the universal Maslov index pulled back along this map

    i *uH 1(Y,). i^\ast u \in H^1(Y,\mathbb{Z}) \,.
    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeSep 18th 2022
    • M. V. Finkelberg, Orthogonal Maslov index, Funct. Anal. Appl. 29(1) 72–74 (1995) doi

    diff, v13, current

    • CommentRowNumber3.
    • CommentAuthorzskoda
    • CommentTimeSep 20th 2022
    • Alan Weinstein, The Maslov cycle as a Legendre singularity and projection of a wavefront set, Bull. Braz. Math. Soc., N.S. 44, 593–610 (2013) doi

    diff, v14, current