Real Algebraic Knots of Low Degree
2011 (English)In: Journal of knot theory and its ramifications, ISSN 0218-2165, Vol. 20, no 9, 1285-1309 p.Article in journal (Refereed) Published
In this paper we study rational real algebraic knots in RP3. We show that two real algebraic knots of degree d<6 are rigidly isotopic if and only if their degrees and encomplexed writhes are equal. We also show that any irreducible smooth knot which admits a plane projection with less than or equal to four crossings has a rational parametrization of degree d<7. Furthermore an explicit construction of rational knots of a given degree with arbitrary encomplexed writhe (subject to natural restrictions) is presented.
Place, publisher, year, edition, pages
2011. Vol. 20, no 9, 1285-1309 p.
Real algebraic knot theory, encomplexed writhe, topology of real algebraic varieties
Research subject Mathematics
IdentifiersURN: urn:nbn:se:uu:diva-156717DOI: 10.1142/S0218216511009248ISI: 000295271700007OAI: oai:DiVA.org:uu-156717DiVA: diva2:432915