论文标题
在具有4个固定点的8维几乎复杂的歧管上的圆圈动作
Circle actions on 8-dimensional almost complex manifolds with 4 fixed points
论文作者
论文摘要
考虑在具有4个固定点的8维紧凑型复杂歧管上进行圆圈动作。据作者所知，$ s^2 \ times s^6 $是这种歧管的唯一已知示例。在本文中，我们证明，如果圆圈在8维紧凑的几乎复杂的歧管$ m $带4个固定点，所有Chern号码和Hirzebruch $χ_y$ genus of $ m $的固定点上都与$ s^2 \ 2 \ times s^6 $一致。尤其是，$ m $是统一的cobordant至$ s^2 \ times s^6 $。
Consider a circle action on an 8-dimensional compact almost complex manifold with 4 fixed points. To the author's knowledge, $S^2 \times S^6$ is the only known example of such a manifold. In this paper, we prove that if the circle acts on an 8-dimensional compact almost complex manifold $M$ with 4 fixed points, all the Chern numbers and the Hirzebruch $χ_y$-genus of $M$ agree with those of $S^2 \times S^6$. In particular, $M$ is unitary cobordant to $S^2 \times S^6$.
