The Bounded Euler Class and the Symplectic Rotation Number

Daiki Uda

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arXiv · 2204.09894

The Bounded Euler Class and the Symplectic Rotation Number

Daiki Uda

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Abstract

Ghys established the relationship between the bounded Euler class in $H_{b}^{2}(\mathrm{Homeo}_{+}(S^{1});\mathbb{Z})$ and the Poincar\'{e} rotation number, that is, he proved that the pullback of the bounded Euler class under a homomorphism $\varphi \colon \mathbb{Z} \to \mathrm{Homeo}_{+}(S^{1})$ coincides with the Poincar\'{e} rotation number of $\varphi(1)$. In this paper, we extend the above result to the symplectic group in some sense, and clarify the relationship between the bounded Euler class in $H_{b}^{2}(Sp(2n;\mathbb{R});\mathbb{Z})$ and the symplectic rotation number investigated by Barge and Ghys.

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Daiki Uda. 2022-04-21. The Bounded Euler Class and the Symplectic Rotation Number. https://arxiv.org/abs/2204.09894

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