Upsilon of L-space knots
download .nb file
This file computes the Upsilon invariant for L-space knots.
- T[p,q] is the (p,q)-torus knot
- TT[p,q,r] is the (p,q)-torus knot with r full twists added
to 2 adjacent strands
- Pretzel[n] is the (-2,3,n) pretzel knot
- Cable[p,q,x] is the (p,q)-cable of the knot x
- More generally, knots can be input by their Alexander
polynomials
The function Upsilon[K] outputs
- The upsilon function of the knot K
- A graph of the linear functions of which upsilon is the
maximum
- A graph of upsilon
- The derivative of upsilon
The function UpsSum[{K_1,...,K_n},{c_1,...,c_n}] outputs
- The upsilon function of the linear combination of knots c_i
K_i (defaults to c_i = 1)
- The graph of upsilon
- The derivative of upsilon
This product was partially supported by NSF grant DMS-1309081.