Special Issue "Symmetry and Beauty of Knots"

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A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: closed (31 December 2011)

Special Issue Editor

Guest Editor
Prof. Dr. Slavik V. Jablan
ICT College, 11000 Belgrade, Zdravka Celara 16, Serbia
Website: http://en.ict.edu.rs/about_us/teaching_staff/jablan_slavik
E-Mail: slavik.jablan@ict.edu.rs
Phone: +381 11 2630170
Fax: +381 11 2186105
Interests: theory of symmetry; antisymmetry; colored symmetry; mathematical crystallography; knot theory; math-art; ornamental art and design; modularity in science and art

Special Issue Information

Dear Colleagues,

Symmetry plays an important role in knot theory for example, every knot or a link has a symmetry group, which is much harder to determine than symmetries of solids since knots and links are considered up to ambient isotopy. Questions like establishing of general criteria for amphicheirality - existence of a left and right form of a knot or link, and invertibility - invariance of a knot under the change of its orientation are still open.

Knots and links appearing in nature have very high degree of summetry, therefore applications of knot theory in chemistry and biology are closely related to studying regular polyhedra (e.g., octahedron corresponding to the Borromean rings), geometry and topology of polyhedral DNA, or knotted Fullerenes - a fast developing area of research. Symmetrical knots and knot patterns such as Celtic knots, are the highlights in the history of art.

Contributions related to various aspects of connections between the theory of symmetry and knot theory are invited. Possible topics include, but are not limited to:

  • symmetry groups of knots, amphicheirality, invertbility and periodicity
  • symmetrical knots in chemistry, biology, art and architecture
  • knot patterns, friezes, Celtic knots, Sona sand drawings, Kolam patterns, decorative knots
  • symmetrical knots on different surfaces and virtual knots
  • knots and quantum computing
  • knots and polyhedra
  • knots and Fulerenes

Prof. Dr. Slavik Jablan
Guest Editor

Published Papers (8 papers)

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Displaying article 1-8
p. 302-328
Article: Knots in Art
by , ,  and
Symmetry 2012, 4(2), 302-328; doi:10.3390/sym4020302
Received: 9 May 2012; in revised form: 15 May 2012 / Accepted: 15 May 2012 / Published: 5 June 2012
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(This article belongs to the Special Issue Symmetry and Beauty of Knots)
p. 285-301
by
Symmetry 2012, 4(2), 285-301; doi:10.3390/sym4020285
Received: 8 March 2012; in revised form: 25 April 2012 / Accepted: 28 April 2012 / Published: 22 May 2012
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(This article belongs to the Special Issue Symmetry and Beauty of Knots)
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p. 276-284
by
Symmetry 2012, 4(2), 276-284; doi:10.3390/sym4020276
Received: 3 February 2012; in revised form: 19 March 2012 / Accepted: 18 April 2012 / Published: 27 April 2012
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(This article belongs to the Special Issue Symmetry and Beauty of Knots)
p. 225-250
by
Symmetry 2012, 4(1), 225-250; doi:10.3390/sym4010225
Received: 3 February 2012; in revised form: 1 March 2012 / Accepted: 1 March 2012 / Published: 7 March 2012
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(This article belongs to the Special Issue Symmetry and Beauty of Knots)
p. 143-207
by , , , , , , , , , ,  and
Symmetry 2012, 4(1), 143-207; doi:10.3390/sym4010143
Received: 4 January 2012; in revised form: 18 January 2012 / Accepted: 31 January 2012 / Published: 20 February 2012
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(This article belongs to the Special Issue Symmetry and Beauty of Knots)
p. 129-142
by , ,  and
Symmetry 2012, 4(1), 129-142; doi:10.3390/sym4010129
Received: 13 January 2012; in revised form: 7 February 2012 / Accepted: 9 February 2012 / Published: 17 February 2012
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(This article belongs to the Special Issue Symmetry and Beauty of Knots)
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p. 39-115
by
Symmetry 2012, 4(1), 39-115; doi:10.3390/sym4010039
Received: 16 November 2011; in revised form: 27 December 2011 / Accepted: 16 January 2012 / Published: 9 February 2012
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(This article belongs to the Special Issue Symmetry and Beauty of Knots)
p. 26-38
by
Symmetry 2012, 4(1), 26-38; doi:10.3390/sym4010026
Received: 14 November 2011; in revised form: 12 January 2012 / Accepted: 13 January 2012 / Published: 20 January 2012
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Last update: 5 March 2014

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