Topological classification of non-degenerate intersections of two ring tori

We study the topological classification of all non-degenerate intersection curves of two arbitrary ring tori. Firstly, all topologically different types of such curves are enumerated. Secondly, an algebraic method is presented for determining the topological type of the non-degenerate intersection curve of two given ring tori. The method works by analyzing the real roots of two univariate quartic polynomials constructed from the two tori.

► We give the topological classification of all non-degenerate intersection curves of two arbitrary ring tori.
► An algebraic method is presented for determining the topological type of the non-degenerate intersection curve of two given ring tori.
► The algebraic method for computation needs only to analyze the real roots of two univariate quartic polynomials constructed from the two tori.