论文标题
有界的欧拉类和符号旋转编号
The Bounded Euler Class and the Symplectic Rotation Number
论文作者
论文摘要
Ghys在$ H_ {B}^{2}（\ Mathrm {homeo} _ {+}（s^{1}）; \ \ Mathbb {z}）$中建立了有限的Euler类之间的关系\ Mathbb {Z} \ to \ Mathrm {HONEO} _ {+}（s^{1}）$与$φ（1）$的Poincaré旋转数量重合。在本文中，我们从某种意义上将上述结果扩展到符号组，并阐明$ H_ {B}^{2}中有界的Euler类之间的关系（sp（2n; \ \ \ Mathbb {r}）; \ Mathbb {z}）$与Barge and Ghys和Ghys调查的符号旋转号。
Ghys established the relationship between the bounded Euler class in $H_{b}^{2}(\mathrm{Homeo}_{+}(S^{1});\mathbb{Z})$ and the Poincaré rotation number, that is, he proved that the pullback of the bounded Euler class under a homomorphism $φ\colon \mathbb{Z} \to \mathrm{Homeo}_{+}(S^{1})$ coincides with the Poincaré rotation number of $φ(1)$. 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.
