On the mean Euler characteristic of contact manifolds
On the mean Euler characteristic of contact manifolds
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DOI：
10.1142/s0129167x14500463
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发表时间：
2010-11
期刊：
影响因子：
--
通讯作者：
J. Espina
中科院分区：
文献类型：
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作者：
J. Espina
对于一类广泛的接触流形，即所谓的渐近有限接触流形，我们用闭Reeb轨道的平均指数来表示接触结构的平均欧拉特性。我们证明了该类在亚临界手术下是封闭的，并检验了在这种手术下平均欧拉特征的行为。为此，我们重新审视联系表单索引正性的概念。我们还得到了莫尔斯-博特情况下的平均欧拉特性的表达式。
We express the mean Euler characteristic of a contact structure in terms of the mean indices of closed Reeb orbits for a broad class of contact manifolds, the so-called asymptotically finite contact manifolds. We show that this class is closed under subcritical surgery and examine the behavior of the mean Euler characteristic under such surgery. To this end, we revisit the notion of index-positivity for contact forms. We also obtain an expression for the mean Euler characteristic in the Morse-Bott case.