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arXiv · 1407.4646

An affirmative answer to a conjecture for Metoki class

Kentaro Mikami
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Abstract

In "The {G}el'fand-{K}alinin-{F}uks class and characteristic classes of transversely symplectic foliations" arXiv:0910.3414, Kotschick and Morita showed that the Gel'fand-Kalinin-Fuks class in $\ds\HGF{7}{2}{}{8}$ is decomposed as a product $\eta\wedge \omega$ of some leaf cohomology class $\eta$ and a transverse symplectic class $\omega$. We show that the same formula holds for Metoki class, which is a non-trivial element in $\ds \HGF{9}{2}{}{14}$. The result was conjectured by Kotschick and Morita, where they studied characteristic classes of symplectic foliations due to Kontsevich. Our proof depends on Groebner Basis theory using computer calculations.

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Kentaro Mikami. 2014-07-17. An affirmative answer to a conjecture for Metoki class. https://arxiv.org/abs/1407.4646

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