SINGULARITY KNOTS OF MINIMAL SURFACES IN R4

We study knots in S-3 obtained by the intersection of a minimal surface in R-4 with a small 3-sphere centered at a branch point. We construct new examples of minimal knots. In particular we show the existence of non-fibered minimal knots. We show that simple minimal knots are either reversible or fully amphicheiral; this yields an obstruction for a given knot to be a simple minimal knot. Properties and invariants of these knots such as the algebraic crossing number of a braid representative and the Alexander polynomial are studied.