In this chapter we shall prove that there exists a finite set of simple, or elementary, moves (also called rules) on labelled apparent contours, such that the following property holds: two images of two stable embeddings of a closed smooth (not necessarily connected) surface are space isotopic if and only if their apparent contours can be connected using finitely many isotopies of the plane, and a finite sequence of elementary moves or of their inverses (sometimes called “reverses”).
Completeness of Reidemeister-Type Moves on Labelled Apparent Contours / Bellettini, Giovanni; Beorchia, Valentina; Paolini, Maurizio; Pasquarelli, Franco. - STAMPA. - 44:(2015), pp. 131-156. [10.1007/978-3-662-45191-5_6]
Completeness of Reidemeister-Type Moves on Labelled Apparent Contours
Beorchia, Valentina;
2015-01-01
Abstract
In this chapter we shall prove that there exists a finite set of simple, or elementary, moves (also called rules) on labelled apparent contours, such that the following property holds: two images of two stable embeddings of a closed smooth (not necessarily connected) surface are space isotopic if and only if their apparent contours can be connected using finitely many isotopies of the plane, and a finite sequence of elementary moves or of their inverses (sometimes called “reverses”).Pubblicazioni consigliate
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