Abstract
We study a certain class of unknotted smooth embeddings of ribbons (i.e., surfaces diffeomorphic to S1×[−1,1]) in Euclidean space R3 (unknotted means that the midline of the ribbon is the unknot). Studying them from the mathematical point of view, we classify them. Regarding them as ideal physical objects with certain properties, we study their behavior under natural conditions. Finally, we discuss the eventual relationship of our models with DNA, RNA, and other long molecules appearing in biophysics.
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