On crossed homomorphisms on symplectic mapping class groups
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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.References
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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
- Received by editor(s): July 26, 2006
- Published electronically: April 11, 2008
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 4815-4839
- MSC (2000): Primary 53C15, 57S05; Secondary 55R40, 57R20
- DOI: https://doi.org/10.1090/S0002-9947-08-04618-7
- MathSciNet review: 2403705