论文标题
Quandle同源性和Cocycle不变性的转移链图
Shifting chain maps in quandle homology and cocycle invariants
论文作者
论文摘要
已经开发了Quandle同源性理论，并已使用Cocycles来定义定向经典或表面链路的不变性。我们在每个Quandle链复合物上引入了一个不断变化的链映射$σ$，该链条将尺寸降低一个。通过使用其下拉$σ^\＃$，每个$ 2 $ -COCYCLE $ ϕ $都为我们提供了$ 3 $ -COCYCLE $σ^\＃ϕ $。对于$ 3 $ - 空间中的定向经典链接，我们探索与$ 2 $ cocycle不变性与$ ϕ $及其阴影$ 3 $ cocycle不变性相关的关系之间的关系。对于$ 4 $ - 空间中的定向表面链接，我们探索了与$σ^\＃ϕ $相关的$ 3 $ cocycle不变性的功能。还讨论了低维（CO）同源组的转移图的代数行为。
Quandle homology theory has been developed and cocycles have been used to define invariants of oriented classical or surface links. We introduce a shifting chain map $σ$ on each quandle chain complex that lowers the dimensions by one. By using its pull-back $σ^\#$, each $2$-cocycle $ϕ$ gives us the $3$-cocycle $σ^\# ϕ$. For oriented classical links in the $3$-space, we explore relation between their quandle $2$-cocycle invariants associated with $ϕ$ and their shadow $3$-cocycle invariants associated with $σ^\# ϕ$. For oriented surface links in the $4$-space, we explore how powerful their quandle $3$-cocycle invariants associated with $σ^\# ϕ$ are. Algebraic behavior of the shifting maps for low-dimensional (co)homology groups is also discussed.
