论文标题
符号Instanton结同源性
Symplectic instanton knot homology
论文作者
论文摘要
Lagrangian Floer同源性不变式的构造中有许多$ 3 $ - manifolds根据Heegaard Slaptings产生的符号性字符品种定义。为了建立Kronheimer和Mrowka的奇异instanton同源性的Atiyah-loer对应物，由于H. Horton，我们将其中之一概括为在一个封闭的，封闭的，方向的$ -MANIFOLD，我们的Intermplect，我们的Inteltect y nemplectemplect，我们的n. knot或link $ k \ subset y $中产生一个lagrangian flovar forner，我们（$ \ mathrm {sik} $）。我们使用多点的Heegaard图来将一对手柄的胶合粘合在一起，并具有正确嵌入的，琐碎的弧形以形成$（y，k）$。这指定了一对无可怜的$ \ mathrm {su}（2）$的Lagrangian嵌入 - $ - 字符的多种刺穿的Heegaard表面，我们表明这具有明确定义的Lagrangian Floer同源性。其不变性证明的一部分是Wehrheim和Woodward的特殊情况，其结果与所谓的基本缠结相关的quil缝浮子同源性，而其他人则将其工作推广到某些非元素缠结。
There have been a number of constructions of Lagrangian Floer homology invariants for $3$-manifolds defined in terms of symplectic character varieties arising from Heegaard splittings. With the aim of establishing an Atiyah-Floer counterpart of Kronheimer and Mrowka's singular instanton homology, we generalize one of these, due to H. Horton, to produce a Lagrangian Floer invariant of a knot or link $K \subset Y$ in a closed, oriented $3$-manifold, which we call symplectic instanton knot homology ($\mathrm{SIK}$). We use a multi-pointed Heegaard diagram to parametrize the gluing together of a pair of handlebodies with properly embedded, trivial arcs to form $(Y, K)$. This specifies a pair of Lagrangian embeddings in the traceless $\mathrm{SU}(2)$-character variety of a multiply punctured Heegaard surface, and we show that this has a well-defined Lagrangian Floer homology. Portions of the proof of its invariance are special cases of Wehrheim and Woodward's results on the quilted Floer homology associated to compositions of so-called elementary tangles, while others generalize their work to certain non-elementary tangles.
