Geodesic
First symplectic Chern class and Maslov indices
Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part V, Tome 143 (1985), pp. 110-129

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An explicit formula is given in this paper for a two-dimensional cocycle in the bar resolution of the group $G=Sp(n,\mathbb R)$, which represents the first Chern class of the natural $n$-dimensional complex vector bundle over $BG^\delta$. It is shown that this cocycle is closely connected with the Maslov indices of Lagrangian subspaces of $\mathbb R^{2n}$. 
@article{ZNSL_1985_143_a5,
     author = {V. G. Turaev},
     title = {First symplectic {Chern} class and {Maslov} indices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {110--129},
     publisher = {mathdoc},
     volume = {143},
     year = {1985},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1985_143_a5/}
}
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V. G. Turaev. First symplectic Chern class and Maslov indices. Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part V, Tome 143 (1985), pp. 110-129. http://geodesic.mathdoc.fr/item/ZNSL_1985_143_a5/