F[U,V]上的Khovanov-Rozansky同调
Khovanov-Rozansky homology over $\mathbb{F}[U,V]$
AI总结：
本文定义了F[U,V]上的完全Khovanov-Rozansky同调链复形CH(K)，证明其链同伦型为纽结不变量，并利用该结构定义了纽结Floer配边不变量τ、ε、φ_j在Khovanov-Rozansky框架下的对应物。
AI中文摘要：
我们定义了Khovanov-Rozansky同调的“完全”版本：一个在F[U,V]上的链复形CH(K)，其链同伦型是纽结不变量，且当U=V=0时可得到约化Khovanov-Rozansky同调。我们探究CH(K)的代数结构，证明纽结Floer同调结构定理的一种变体适用，这使我们能在Khovanov-Rozansky框架下定义纽结Floer配边不变量τ、ε和φ_j的对应物。
英文摘要：
We define a 'full' version of Khovanov-Rozansky homology: a chain complex CH(K) over F[U,V] whose chain homotopy type is a knot invariant and which has the property that setting U = V = 0 recovers the reduced Khovanov-Rozansky homology. We explore the algebraic structure of CH(K) and show that a variation of the structure theorem for knot Floer homology applies. This allows us to define counterparts to knot Floer concordance invariants $τ$, $ε$ and $ϕ_j$ in the Khovanov-Rozansky setting.
