Study on quandle theory to classifying links up to link-homotopy

链接同伦在链接上产生等价关系，这种等价关系弱于环境同位素。quandle是一个代数系统，它被认为是有用的分类链接到环境同位素。本研究的目的是利用量子点对链路进行分类直至链路同伦。引入了准平凡量子的概念，准平凡量子的同调理论，得到了大量的数值连杆同伦不变量。我们进一步解释了这些不变量的潜在能力。

Link-homotopy gives rise to an equivalence relation on links which is weaker than ambient isotopy. A quandle is an algebraic system which is known to be useful to classifying links up to ambient isotopy. The aim of this study is to utilize quandles to classifying links up to link-homotopy. We introduced the notion of quasi-triviality of quandles, homology theory for quasi-trivial quandles, and obtained a lot of numerical link-homotopy invariants. We further explained the latent ability of those invariants.