NONTRIVIAL EMBEDDINGS OF POLYGONAL INTERVALS AND UNKNOTS IN 3-SPACE

Abstract

We consider embedding classes of polygonal intervals and circles with fixed edge lengths. We classify all embeddings of polygonal lines of five segments, finding that this space has three connected components for suitable edge lengths. We then construct a class of "stuck" unknotted hexagons, which cannot be deformed to the standard unknotted hexagon. The edge lengths of our examples are not equal.