Special Issue "Symmetry and Beauty of Knots"
A special issue of Symmetry (ISSN 2073-8994).
Deadline for manuscript submissions: closed (31 December 2011)
Prof. Dr. Slavik V. Jablan
ICT College, 11000 Belgrade, Zdravka Celara 16, Serbia
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
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