论文标题
涉及打结浮子同源性和边界模块
Involutive knot Floer homology and bordered modules
论文作者
论文摘要
我们证明，到达局部等效性，在$ s^3 $中的结节涉及结式同源性的合适截断以及其补充的Heegaard Floer理论相互决定的。特别是，给定两个节$ k_1 $和$ k_2 $，我们证明$ \ mathbb {f} _2 [u，v]/（uv）/（uv）$ - 系数涉及$ k_1 \ k_1 \ sharp -k_2 $ sharp -k_2 $ as $ k_2 $ as $ k $ blocial-locial-if tif $ wif $ - $ \ wideHat {cfd}（s^2 \ backslash k_2）$满足某种条件，该条件可以看作是$ 〜B $ - $ - 局部等价的边界对应物。我们进一步建立了一个明确的代数公式，该公式可以计算出来自其补充的涉及的边界的浮子同源性的结的涉及结式浮子同源性的帽子味的截断。因此，存在一个代数卫星操作员，该代数卫星运算符在局部的结式链链络合物组上定义，可以将其明确计算为合适的截断。
We prove that, up to local equivalences, a suitable truncation of the involutive knot Floer homology of a knot in $S^3$ and the involutive bordered Heegaard Floer theory of its complement determine each other. In particular, given two knots $K_1$ and $K_2$, we prove that the $\mathbb{F}_2[U,V]/(UV)$-coefficient involutive knot Floer homology of $K_1 \sharp -K_2$ is $ι_K$-locally trivial if $\widehat{CFD}(S^3 \backslash K_1)$ and $\widehat{CFD}(S^2 \backslash K_2)$ satisfy a certain condition which can be seen as the bordered counterpart of $ι_K$-local equivalence. We further establish an explicit algebraic formula that computes the hat-flavored truncation of the involutive knot Floer homology of a knot from the involutive bordered Floer homology of its complement. It follows that there exists an algebraic satellite operator defined on the local equivalence group of knot Floer chain complexes, which can be computed explicitly up to a suitable truncation.
