In mathematical knot theory, a Conway sphere, named after John Horton Conway, is a 2-sphere intersecting a given knot or link in a 3-manifold transversely in four points. In a knot diagram, a Conway sphere can be represented by a simple closed curve crossing four points of the knot, the cross-section of the sphere; such a curve does not always exist for an arbitrary knot diagram of a knot with a Conway sphere, but it is always possible to choose a diagram for the knot in which the sphere can be depicted in this way. A Conway sphere is essential if it is incompressible in the knot complement.[1] Sometimes, this condition is included in the definition of Conway spheres.[2]
References
[edit]- ^ Gordon, Cameron McA.; Luecke, John (2006). "Knots with unknotting number 1 and essential Conway spheres". Algebraic & Geometric Topology. 6 (5): 2051–2116. arXiv:math/0601265. Bibcode:2006math......1265M. doi:10.2140/agt.2006.6.2051.
- ^ Lickorish, W. B. Raymond (1997), An introduction to knot theory, Graduate Texts in Mathematics, vol. 175, Berlin, New York: Springer-Verlag, ISBN 978-0-387-98254-0, MR 1472978
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Well, that’s interesting to know that Psilotum nudum are known as whisk ferns. Psilotum nudum is the commoner species of the two. While the P. flaccidum is a rare species and is found in the tropical islands. Both the species are usually epiphytic in habit and grow upon tree ferns. These species may also be terrestrial and grow in humus or in the crevices of the rocks.
View the detailed Guide of Psilotum nudum: Detailed Study Of Psilotum Nudum (Whisk Fern), Classification, Anatomy, Reproduction