标题： 接触手术数的射影空间 显示英文标题

标题： Contact surgery numbers of projective spaces

摘要： 我们将所有接触手术数为一的接触射影空间分类。 特别地，这表明在实射影3-空间上存在无穷多个非同痕的接触结构，它们无法通过单一有理接触手术从标准的密接接触3-球得到。 我们的证明中有很大一部分涉及对Gompf关于三维流形切触平面场的$\Gamma$不变量的详细分析。 从我们的主要结果我们还推导出，实射影3-空间上切触平面场的$\Gamma$不变量仅依赖于其$d_3$不变量。 显示英文摘要

摘要： We classify all contact projective spaces with contact surgery number one. In particular, this implies that there exist infinitely many non-isotopic contact structures on the real projective 3-space which cannot be obtained by a single rational contact surgery from the standard tight contact 3-sphere. Large parts of our proofs deal with a detailed analysis of Gompf's $\Gamma$-invariant of tangential 2-plane fields on 3-manifolds. From our main result we also deduce that the $\Gamma$-invariant of a tangential 2-plane field on the real projective 3-space only depends on its $d_3$-invariant.