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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Remarks on the homotopy type of groups of symplectic diffeomorphisms


Author: Dusa McDuff
Journal: Proc. Amer. Math. Soc. 94 (1985), 348-352
MSC: Primary 58D05; Secondary 53C15, 57R50
MathSciNet review: 784191
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Abstract: Let $ (X,\omega )$ be a symplectic manifold without boundary, $ G(X)$ the identity component of its group of compactly supported diffeomorphisms, and $ {H_\omega }(X)$ the subgroup of $ G(X)$ consisting of all symplectic diffeomorphisms. In this note, we give examples in which $ {H_\omega }(X)$ is not homotopy equivalent to $ G(X)$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0784191-0
PII: S 0002-9939(1985)0784191-0
Keywords: Symplectic diffeomorphism, groups of diffeomorphisms
Article copyright: © Copyright 1985 American Mathematical Society