Topology and Geometry in Polymer Science pp 49-65 | Cite as

# Energy and Thickness of Knots^{*}

## Abstract

Knots in real physical systems, be they rope or DNA loops, have real physical properties; that is a truism. The behavior of *physical knots* depends on the topological types of the knots; that is an experimental observation. Mathematical differences between knot types and, more generally, the whole body of knot theory should help explain the physical behavior; that is a hope. If we make the three simplest knots out of similar “rope” having the same lengths Figure 1, we see that one kind of knot seems more “tight” or “compact” than another. Somehow this difference will manifest itself in physical systems and should be predictable from the topology.

## Keywords

World Scientific Special Session Summer Program Real Physical System Edge Number## Preview

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