53 pages, 4 figures, with an appendix by Michael Hutchings; v.3 is a final update to agree with the published paper, and also corrects a minor error that appeared in the published version of the appendix
We extract a nonnegative integer-valued invariant, which we call the "order of algebraic torsion", from the Symplectic Field Theory of a closed contact manifold, and show that its finiteness gives obstructions to the existence of symplectic fillings and exact symplectic cobordisms. A contact manifold has algebraic torsion of order zero if and only if it is algebraically overtwisted (i.e. has trivial contact homology), and any contact 3-manifold with positive Giroux torsion has algebraic torsion of order one (though the converse is not true). We also construct examples for each nonnegative k of contact 3-manifolds that have algebraic torsion of order k but not k - 1, and derive consequences for contact surgeries on such manifolds. The appendix by Michael Hutchings gives an alternative proof of our cobordism obstructions in dimension three using a refinement of the contact invariant in Embedded Contact Homology.
我们使用缝合TQFT的理论来分类接触元素的缝合弗洛尔同调，$\Z$系数，某些缝合流形的形式$(Σ\times S^1, F \times S^1)$其中$Σ$是一个环或穿孔环面。利用这一分类，我们给出了一个新的证明，证明了具有Giroux挠率的切触结构与$\Z$系数的缝合弗洛尔同调调中的接触不变量为零.我们还给出了Massot定理的一个新的证明，即对于由隔离分割集描述的$(Σ\times S^1, F \times S^1)$上的切触结构，接触不变量为零。
我们证明了切触同调区分了任意可定向的、环面的、不可约的3-流形上的无穷多个紧切触结构。作为接触同调计算的结果，在一个非常大的类的环面流形，所有已知的例子普遍紧切触结构与非零挠满足温斯坦猜想。- 关于montre que l 'homologie de contact distingue une infinite de structures de contact tendues sur toute variete toroidale irreductible et orientable de dimensions trois。通过对一个三大类变截面环的接触的同调计算，证明了温斯坦的猜想与接触结构的普遍扭转趋势无关。
