Characteristic numbers, Jiang subgroup and non-positive curvature

Abstract

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 ${\chi }_y$-genus on compact smooth and Kähler manifolds respectively. Along this line we show that the ${\chi }_y$-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.

14 pages

Cited by in corpus (1)

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