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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}) \,.
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