Torsion structures in triangulated categories

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We focused on torsion pairs in triangulated categories. Torsion pairs are basic framework in representation theory. They enable us to decompose a given triangulated category into subcategories. We aimed at studying mechanism of existing "good" torsion pairs and applying them. We have obtained the following results: (1) discovery of a "triangle of recollements" which induces high symmetry and a new triangle equivalence as an application. (2) introducing homotopy and derived categories of "n-complexes" and triangle equivalence of these categories to homotopy and derived categories of normal complexes over a suitable extension ring. (3) one to one correspondence of weak torsion pairs to torsion pairs in a quotient category.