Motivated by work of Fine and Panov, and of Lindsay and Panov, we prove that every closed symplectic complexity one space that is positive (e.g., positive monotone) enjoys topological properties that Fano varieties with a complexity one holomorphic torus action possess. In particular, such spaces are simply connected, have Todd genus equal to one and vanishing odd Betti numbers.

中文翻译：

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正复杂性一空间的拓扑性质

由Fine和Panov以及Lindsay和Panov的工作所激发，我们证明了，每个封闭辛辛复杂性，一个为正的空间（例如，正单调）都具有Fano变体的拓扑特性，而Fano变种具有一个全同圆环作用。特别地，这样的空间简单地连接，具有等于1的Todd属并且消失的奇数Betti数。