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

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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.