Let a $k$-dimensional torus $T^k$ act on a $2n$-dimensional compact connected almost complex manifold $M$ with isolated fixed points. As in the case of circle actions, we show that there exists a (directed labeled) multigraph that contains information on weights at the fixed points and isotropy submanifolds of $M$. This includes the notion of a GKM (Goresky-Kottwitz-MacPherson) graph as a special case that weights at each fixed point are pairwise linearly independent. If in addition $k=n$, that is, $M$ is an almost complex torus manifold, the multigraph is a graph; it has no multiple edges. We show that the Hirzebruch $\chi _y$-genus $\chi _y(M)=\sum _{i=0}^n a_i(M) \cdot (-y)^i$ of an almost complex torus manifold $M$ satisfies $a_i(M)> 0$ for $0 \leq i \leq n$. In particular, the Todd genus of $M$ is positive and there are at least $n+1$ fixed points.

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几乎复杂的圆环流形——图和 Hirzebruch Genera

让一个$k$ 维环面$T^k$ 作用于一个$2n$ 维紧凑连接的几乎复流形$M$ 与孤立的固定点。与圆形动作的情况一样，我们表明存在一个（有向标记）多重图，其中包含有关 $M$ 的固定点和各向同性子流形的权重信息。这包括 GKM（Goresky-Kottwitz-MacPherson）图的概念，作为每个固定点的权重成对线性独立的特殊情况。如果再加上$k=n$，即$M$是一个几乎复数的环面流形，则多重图是一个图；它没有多重边。我们证明了几乎复数环面流形 $ 的 Hirzebruch $\chi _y$-genus $\chi _y(M)=\sum _{i=0}^n a_i(M) \cdot (-y)^i$ M$满足$a_i(M)> 0$ 为 $0 \leq i \leq n$。尤其是，