Seifert Surface

An orientable surface with one boundary component such that the boundary component of the surface is a given Knot . In 1934, Seifert proved that such a surface can be constructed for any Knot. The process of generating this surface isknown as Seifert's algorithm. Applying Seifert's algorithm to an alternating projection of an alternating knot yields aSeifert surface of minimal Genus.

There are Knots for which the minimal genus Seifert surface cannot be obtained by applying Seifert's algorithmto any projection of that Knot, as proved by Morton in 1986 (Adams 1994, p. 105).

References

Adams, C. C. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. New York: W. H. Freeman, pp. 95-106, 1994.

Seifert, H. ``Über das Geschlecht von Knotten.'' Math. Ann. 110, 571-592, 1934.

• Prime Quadratic Effect
• Prime Quadruplet
• Prime Representation
• Prime Ring
• Prime Sequence
• Prime Spiral
• Prime String
• Prime Sum
• Prime Theta Function
• Prime Triangle
• Prime Unit
• Prime Zeta Function
• Primitive Abundant Number
• Primitive Function
• Primitive Irreducible Polynomial
• Primitive Polynomial Modulo 2
• Primitive Prime Factor
• Primitive Pseudoperfect Number
• Primitive Recursive Function
• Primitive Root
• Primitive Root of Unity
• Primitive Semiperfect Number
• Primitive Sequence
• Primorial
• Prince Rupert's Cube