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Zap. Nauchn. Sem. LOMI, 1985, Volume 143, Pages 110–129 (Mi znsl4919)  

First symplectic Chern class and Maslov indices

V. G. Turaev


Abstract: 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 $\mathbb R^{2n}$.

Full text: PDF file (1029 kB)

English version:
Journal of Soviet Mathematics, 1987, 37:3, 1115–1127

Bibliographic databases:

UDC: УДК 517.43

Citation: V. G. Turaev, “First symplectic Chern class and Maslov indices”, Investigations in topology. Part V, Zap. Nauchn. Sem. LOMI, 143, "Nauka", Leningrad. Otdel., Leningrad, 1985, 110–129; J. Soviet Math., 37:3 (1987), 1115–1127

Citation in format AMSBIB
\Bibitem{Tur85}
\by V.~G.~Turaev
\paper First symplectic Chern class and Maslov indices
\inbook Investigations in topology. Part~V
\serial Zap. Nauchn. Sem. LOMI
\yr 1985
\vol 143
\pages 110--129
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl4919}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=806563}
\zmath{https://zbmath.org/?q=an:0577.55012}
\transl
\jour J. Soviet Math.
\yr 1987
\vol 37
\issue 3
\pages 1115--1127
\crossref{https://doi.org/10.1007/BF01086635}


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