Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57R20, 58F05

Retrieve articles in all journals with MSC: 57R20, 58F05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1124152-X
PII: S 0002-9939(1993)1124152-X
Keywords: Chern-Simons-Maslov classes, symplectic, Lagrangian, connections, curvatures
Article copyright: © Copyright 1993 American Mathematical Society