论文标题
Lipshitz-ozsváth-Thurston对应的助记符
A mnemonic for the Lipshitz-Ozsváth-Thurston correspondence
论文作者
论文摘要
当$ \ mathbf {k} $是一个字段时，代数$ \ mathbf {k} [u，v]/（uv）/（uv）$上的类型D结构等同于在两次启动磁盘中装饰有本地系统的沉浸式曲线。因此，打结浮子同源性，作为$ \ mathbf {k} [u，v]/（uv）$的D型结构，可以看作是一组沉浸式曲线。 With this observation as a starting point, given a knot $K$ in $S^3$, we realize the immersed curve invariant $\widehat{\mathit{HF}}(S^3 \smallsetminus \mathringν(K))$ [arXiv:1604.03466] by converting the twice-punctured disk to a once-punctured torus via a handle attachment.这恢复了Lipshitz，Ozsváth和Thurston [Arxiv：0810.0687]在打结的$ k $的结floer同源性方面计算$ s^3 \ SmallSetMinus \ MathingMining（K）$的边界不变。
When $\mathbf{k}$ is a field, type D structures over the algebra $\mathbf{k}[u,v]/(uv)$ are equivalent to immersed curves decorated with local systems in the twice-punctured disk. Consequently, knot Floer homology, as a type D structure over $\mathbf{k}[u,v]/(uv)$, can be viewed as a set of immersed curves. With this observation as a starting point, given a knot $K$ in $S^3$, we realize the immersed curve invariant $\widehat{\mathit{HF}}(S^3 \smallsetminus \mathringν(K))$ [arXiv:1604.03466] by converting the twice-punctured disk to a once-punctured torus via a handle attachment. This recovers a result of Lipshitz, Ozsváth, and Thurston [arXiv:0810.0687] calculating the bordered invariant of $S^3 \smallsetminus \mathringν(K)$ in terms of the knot Floer homology of $K$.
