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
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*
{{knottheory-stub
Knot invariants