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Real Algebraic Knots of Low Degree
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Geometry and Logic. (Topology)
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
Abstract [en]

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.
Keyword [en]
Real algebraic knot theory, encomplexed writhe, topology of real algebraic varieties
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Research subject
URN: urn:nbn:se:uu:diva-156717DOI: 10.1142/S0218216511009248ISI: 000295271700007OAI: oai:DiVA.org:uu-156717DiVA: diva2:432915
Available from: 2011-08-08 Created: 2011-08-08 Last updated: 2012-02-16Bibliographically approved

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Björklund, Johan
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Algebra, Geometry and Logic
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