In this paper we are concerned with labelled apparent contours, namely with apparent contours of generic orthogonal projections of embedded surfaces in R3, 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 S in R3 are isotopic if and only if their apparent contours can be connected using only smooth isotopies and a finite sequence of moves.

Paolini, M., Bellettini, G., Beorchia, V., Completeness of Reidemeister-type moves for surfaces embedded in three-dimensional space, <<ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI>>, 2012; (23): 69-87. [doi:10.4171/RLM/617] [http://hdl.handle.net/10807/18643]

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

Paolini, Maurizio;Bellettini, Giovanni;Beorchia, Valentina
2012

Abstract

In this paper we are concerned with labelled apparent contours, namely with apparent contours of generic orthogonal projections of embedded surfaces in R3, 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 S in R3 are isotopic if and only if their apparent contours can be connected using only smooth isotopies and a finite sequence of moves.
Inglese
Paolini, M., Bellettini, G., Beorchia, V., Completeness of Reidemeister-type moves for surfaces embedded in three-dimensional space, <<ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI>>, 2012; (23): 69-87. [doi:10.4171/RLM/617] [http://hdl.handle.net/10807/18643]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10807/18643
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