Calculus of Variations and Geometric Measure Theory

G. Bellettini - V. Beorchia - M. Paolini

Completeness of Reidemeister-type moves for surfaces embedded in three-dimensional space

created by belletti on 27 Jan 2009


Submitted Paper

Inserted: 27 jan 2009

Year: 2009


In this paper we are concerned with labelled apparent contours, namely with apparent contours of generic orthogonal projections of embedded surfaces in $\R^3$, endowed with a suitable depth information. We show that there exists a finite set of elementary moves (i.e. local topological changes) on labelled apparent contours such that the following theorem holds: two generic embeddings of a closed surface $\referencemanifold$ in $\R^3$ are isotopic if and only if their apparent contours can be connected using only smooth isotopies and a finite sequence of moves.