一个推广的Gompf不变量的变分公式
Variation formulas for an extended Gompf invariant
摘要：
1998年，R. Gompf定义了三维流形中定向2-平面场的同伦不变量$θ_G$.当第一个Chern类$c_1(ξ)$是$H^2(M;\mathbb{Z})$的扭元时，定义了闭定向三维流形$M$中定向2平面场$ξ$的不变量.本文定义了所有紧定向三维流形的Gompf不变量的一个扩张，并研究了它在保拉格朗日变换下的迭代变分。由此可知，推广的Gompf不变量对于合适的有限型不变量理论是二阶不变量.
英文摘要：
In 1998, R. Gompf defined a homotopy invariant $θ_G$ of oriented 2-plane fields in 3-manifolds. This invariant is defined for oriented 2-plane fields $ξ$ in a closed oriented 3-manifold $M$ when the first Chern class $c_1(ξ)$ is a torsion element of $H^2(M;\mathbb{Z})$. In this article, we define an extension of the Gompf invariant for all compact oriented 3-manifolds with boundary and we study its iterated variations under Lagrangian-preserving surgeries. It follows that the extended Gompf invariant is a degree two invariant with respect to a suitable finite type invariant theory.
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