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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Chern-Simons-Maslov classes of some symplectic vector bundles

Author: Haruo Suzuki
Journal: Proc. Amer. Math. Soc. 117 (1993), 541-546
MSC: Primary 57R20; Secondary 58F05
MathSciNet review: 1124152
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Abstract: Let $ {E_0},\;{J_0}$, and $ {L_0}$ be the symplectic $ 2n$-vector bundle, the compatible complex operator, and the Lagrangian subbundle that are determined by the $ U(n)$-extension of the principal $ O(n)$-bundle $ U(n) \to U(n)/O(n)$. We compute the Chern-Simons-Maslov class $ {\mu ^1}({E_0},{J_0},{L_0})$. Then for a trivial symplectic $ 2n$-bundle $ E$, a compatible complex operator $ J$, and a Lagrangian subbundle $ L$, we compute Chern-Simons-Maslov classes $ {\mu ^h}(E,J,L)$ under some condition on the base space of $ E$.

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Keywords: Chern-Simons-Maslov classes, symplectic, Lagrangian, connections, curvatures
Article copyright: © Copyright 1993 American Mathematical Society

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