论文标题
Instanton Floer同源性I：主要定理的结节手术公式
Knot surgery formulae for instanton Floer homology I: the main theorem
论文作者
论文摘要
我们证明了用于框架的Instanton同源性的整体手术配方$ i^\ sharp（y_m（k））$ in a $ 3 $ -manifold $ y $中的任何结$ k $ in h_1（y; \ mathbb {q}）$ in $ 3 $ -manifold $ y $，n $ [k] = 0 \ n h_1（y; \ mathbb {q}）$和$ m \ neq 0 $。尽管该声明类似于Ozsváth-Szabó针对Heegaard Floer同源性的整体手术公式，但该证明是新的，并且基于缝合的Instanton同源性$ SHI $和派生类别中的八面体引理。作为推论，我们在$ i^\ sharp（y_m（k））$，$ i^\ sharp（y_ {m+k}（k））$和$ k $副本$ i^\ sharp（y sharp（y）$ of $ m \ m \ neq 0 $和大$ k $之间。在公式的证明中，我们发现了许多用于缝合的插入式同源性的新的精确三角形，并将一些手术的恢复图与旁路图的总和相关联，这些图具有独立的关注。在同伴论文中，我们根据整体手术公式得出了许多应用和计算。
We prove an integral surgery formula for framed instanton homology $I^\sharp(Y_m(K))$ for any knot $K$ in a $3$-manifold $Y$ with $[K]=0\in H_1(Y;\mathbb{Q})$ and $m\neq 0$. Though the statement is similar to Ozsváth-Szabó's integral surgery formula for Heegaard Floer homology, the proof is new and based on sutured instanton homology $SHI$ and the octahedral lemma in the derived category. As a corollary, we obtain an exact triangle between $I^\sharp(Y_m(K))$, $I^\sharp(Y_{m+k}(K))$ and $k$ copies of $I^\sharp(Y)$ for any $m\neq 0$ and large $k$. In the proof of the formula, we discover many new exact triangles for sutured instanton homology and relate some surgery cobordism map to the sum of bypass maps, which are of independent interest. In a companion paper, we derive many applications and computations based on the integral surgery formula.
