Knot invariants, normal surfaces and integer programming
by Ben Burton
Abstract: The crosscap number of a knot is an invariant that is difficult to compute, and for which no general algorithm is known. In this talk we discuss two new methods for computing crosscap numbers based on normal surfaces. One involves a streamlined enumeration of the Hilbert basis for a pointed rational cone; the other formulates the problem using exact integer programming. Although both methods may give indeterminate results in some cases, in practice they yield 191 new crosscap numbers that were previously unknown.