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

Maurizio Paolini, Giovanni Bellettini, Valentina Beorchia

Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer review

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.
Lingua originaleEnglish
pagine (da-a)69-87
Numero di pagine19
RivistaATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI
DOI
Stato di pubblicazionePubblicato - 2012

Keywords

  • Apparent contours
  • topology of embedded surfaces

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