论文标题
符号三触角和邻接不等式
Symplectic trisections and the adjunction inequality
论文作者
论文摘要
在本文中，我们为封闭的symbletic 4-manifolds建立了一个邻接不平等的版本。与以前关于汤姆（Thom）猜想的论文一样，我们使用触点几何形状和4个manifolds的三分法将这种不平等降低到4球中的打结的斜线不平等。由于可以使用Khovanov同源性证明后一个结果，因此我们完全避免了理论技术。这种不平等可用于给出几个地标的量规证明，从而导致4个manifold拓扑结构，例如检测异国情调的平滑结构，象征性的thom猜想以及某些符号4个manifolds的连接的总和分解。
In this paper, we establish a version of the adjunction inequality for closed symplectic 4-manifolds. As in a previous paper on the Thom conjecture, we use contact geometry and trisections of 4-manifolds to reduce this inequality to the slice-Bennequin inequality for knots in the 4-ball. As this latter result can be proved using Khovanov homology, we completely avoid gauge theoretic techniques. This inequality can be used to give gauge-theory-free proofs of several landmark results in 4-manifold topology, such as detecting exotic smooth structures, the symplectic Thom conjecture, and exluding connected sum decompositions of certain symplectic 4-manifolds.
