论文标题
特征数，江亚组和非阳性曲率
Characteristic numbers, Jiang subgroup and non-positive curvature
论文作者
论文摘要
通过完善Farrell的想法，我们在江型亚组方面提出了足够的条件，用于消失签名和Hirzebruch的$χ_y$ genus，分别在紧凑型和Kähler歧管上。沿着这条线，我们表明，当其基本群体的中心是非平凡时，非物性弯曲紧凑的Kähler歧管的$χ_y$ genus消失了，这部分回答了Farrell的问题。此外，在后一种情况下，每当Chern数字的复杂尺寸不超过$ 4 $，所有Chern数字都消失了，这也为作者和Zheng提出的猜想提供了一些证据。
By refining an idea of Farrell, we present a sufficient condition in terms of the Jiang subgroup for the vanishing of signature and Hirzebruch's $χ_y$-genus on compact smooth and Kähler manifolds respectively. Along this line we show that the $χ_y$-genus of a non-positively curved compact Kähler manifold vanishes when the center of its fundamental group is non-trivial, which partially answers a question of Farrell. Moreover, in the latter case all the Chern numbers vanish whenever its complex dimension is no more than $4$, which also provides some evidence to a conjecture proposed by the author and Zheng.
