论文标题
打结浮子同源性和相对的邻接不平等现象
Knot Floer homology and relative adjunction inequalities
论文作者
论文摘要
我们建立了不平等的不平等，以限制4维同步性结中的平滑恢复属。这些“相对辅助不平等”改善了封闭表面的邻接不平等现象，这些封闭表面在仪表理论的许多拓扑应用中都具有重要作用。相对不等式通过将结的数值不变性在与Heegaard Floer同源性类别相关的边界中结合在一起，从而完善了后者。作为推论，我们在一般的3型曼尼弗中生成了许多不变的结，对于每个非零的浮子类都这样一个不变。我们应用结果来产生Ozsváth-Szabó-rasmussen的类似物，以使链接不变，从而使我们能够谴责Milnor猜想的链接版本，此外，还可以表明，结Floer同源性检测到牢固地进行了清晰的纤维启动链接。
We establish inequalities that constrain the genera of smooth cobordisms between knots in 4-dimensional cobordisms. These "relative adjunction inequalities" improve the adjunction inequalities for closed surfaces which have been instrumental in many topological applications of gauge theory. The relative inequalities refine the latter by incorporating numerical invariants of knots in the boundary associated to Heegaard Floer homology classes determined by the 4-manifold. As a corollary, we produce a host of concordance invariants for knots in a general 3-manifold, one such invariant for every non-zero Floer class. We apply our results to produce analogues of the Ozsváth-Szabó-Rasmussen concordance invariant for links, allowing us to reprove the link version of the Milnor conjecture, and, furthermore, to show that knot Floer homology detects strongly quasipositive fibered links.
