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. It is essential if it is incompressible in the knot complement.[1] Sometimes, this condition is included in the definition of Conway spheres.[2]
References
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, 175, Berlin, New York: Springer-Verlag, ISBN 978-0-387-98254-0, MR 1472978
Knot theory (knots and links)
Hyperbolic
Figure-eight (41) Three-twist (52) Stevedore (61) 62 63 Endless (74) Carrick mat (818) Perko pair (10161) (−2,3,7) pretzel (12n242) Whitehead (52
1) Borromean rings (63
2) L10a140
Satellite
Composite knots
Granny Square Knot sum
Torus
Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02
1) Hopf (22
1) Solomon's (42
1)
Invariants
Alternating Arf invariant Bridge no.
2-bridge Brunnian Chirality
Invertible Crosscap no. Crossing no. Finite type invariant Hyperbolic volume Khovanov homology Genus Knot group Link group Linking no. Polynomial
Alexander Bracket HOMFLY Jones Kauffman Pretzel Prime
list Stick no. Tricolorability Unknotting no. and problem
Notation
and operations
Alexander–Briggs notation Conway notation Dowker notation Flype Mutation Reidemeister move Skein relation Tabulation
Other
Alexander's theorem Berge Braid theory Conway sphere Complement Double torus Fibered Knot List of knots and links Ribbon Slice Sum Tait conjectures Twist Wild Writhe Surgery theory
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
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