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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On crossed homomorphisms on symplectic mapping class groups


Author: Ryoji Kasagawa
Journal: Trans. Amer. Math. Soc. 360 (2008), 4815-4839
MSC (2000): Primary 53C15, 57S05; Secondary 55R40, 57R20
Published electronically: April 11, 2008
MathSciNet review: 2403705
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Abstract: For a symplectic manifold $ (M,\omega)$ with a relation $ Q$ between Chern classes of it and the cohomology class of the symplectic form $ \omega$, we construct a crossed homomorphism $ F_Q$ on the symplectomorphism group of $ (M,\omega)$ with values in the cohomology group of $ M$ and show an application to the symplectic flux group. Moreover we see that $ F_Q$ descends to a crossed homomorphism on the symplectic mapping class group of $ (M,\omega)$ and show a nontrivial example of it.


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Additional Information

Ryoji Kasagawa
Affiliation: Department of Mathematics, College of Science and Technology, Nihon University, 1-8 Kanda, Surugadai, Chiyoda-ku, Tokyo 101-8308, Japan
Email: kasagawa@math.cst.nihon-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04618-7
PII: S 0002-9947(08)04618-7
Received by editor(s): July 26, 2006
Published electronically: April 11, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.