论文标题
中级RICCI曲率和Gromov的Betti数字约束
Intermediate Ricci curvatures and Gromov's Betti number bound
论文作者
论文摘要
我们考虑封闭的Riemannian歧管$ M^n $上的中级RICCI曲率$ ric_k $。当$ k = n-1 $和$ k = 1 $时，当$ k = n-1 $和截面曲率时，这些插值在RICCI曲率之间。通过建立$ ric_k> 0 $的Riemannian指标的手术结果，我们表明Gromov在下面界定的截面曲率的上贝蒂数字限制为$ ric_k> 0 $时，当$ ric_k> 0 $时，当$ \ lfloor n/2 \ rfloor+rfloor+2 \ le l le k \ le k \ le n-1 $。以前仅在RICCI曲率的情况下才知道这一点。
We consider intermediate Ricci curvatures $Ric_k$ on a closed Riemannian manifold $M^n$. These interpolate between the Ricci curvature when $k=n-1$ and the sectional curvature when $k=1$. By establishing a surgery result for Riemannian metrics with $Ric_k>0$, we show that Gromov's upper Betti number bound for sectional curvature bounded below fails to hold for $Ric_k>0$ when $\lfloor n/2 \rfloor+2 \le k \le n-1$. This was previously known only in the case of positive Ricci curvature.
