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arXiv · 2205.04937

Characteristic numbers, Jiang subgroup and non-positive curvature

Ping Li
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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 K\"{a}hler manifolds respectively. Along this line we show that the $\chi_y$-genus of a non-positively curved compact K\"{a}hler 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.

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Ping Li. 2022-05-10. Characteristic numbers, Jiang subgroup and non-positive curvature. https://doi.org/10.1007/s00209-022-03162-w

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