Computing the Crosscap Number of a Knot Using Integer Programming and Normal Surfaces
Computing the Crosscap Number of a Knot Using Integer Programming and Normal Surfaces
The crosscap number of a knot is an invariant describing the non-orientable surface of smallest genus that the knot bounds. Unlike knot genus (its orientable counterpart), crosscap numbers are difficult to compute and no general algorithm is known. We present three methods for computing crosscap number that offer varying trade-offs …