Thurston–Bennequin Number
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In the mathematical theory of knots, the Thurston–Bennequin number, or Bennequin number, of a front diagram of a Legendrian knot is defined as the writhe of the diagram minus the number of right
cusp A cusp is the most pointed end of a curve. It often refers to cusp (anatomy), a pointed structure on a tooth. Cusp or CUSP may also refer to: Mathematics * Cusp (singularity), a singular point of a curve * Cusp catastrophe, a branch of bifu ...
s. It is named after
William Thurston William Paul Thurston (October 30, 1946August 21, 2012) was an American mathematician. He was a pioneer in the field of low-dimensional topology and was awarded the Fields Medal in 1982 for his contributions to the study of 3-manifolds. Thurst ...
and
Daniel Bennequin Daniel Bennequin (3 January 1952) is a French mathematician, known for the Thurston–Bennequin number (sometimes called the Bennequin number) introduced in his doctoral dissertation. Education and career Bennequin completed his secondary educati ...
. The maximum Thurston–Bennequin number over all Legendrian representatives of a knot is a topological
knot invariant In the mathematical field of knot theory, a knot invariant is a quantity (in a broad sense) defined for each knot which is the same for equivalent knots. The equivalence is often given by ambient isotopy but can be given by homeomorphism. Some i ...
.


References

* * {{knottheory-stub Knot invariants