Mathematical Knots

"The Topology of Knots" was the title of an address given to the Maths, and Physics Society by Mr W. Malcolm. He explained that in characterising knots mathematically we are interested in those properties which remain invarient under continuous or "rubber sheet" transformations. Such transformations can be represented analytically so we have precise concepts for the treating of knots. An explanation was given of a property of polyhedra invarient under continuous transformations, the Euler-Poincare relation, and how by a construction, this property can be used to characterise knots. It turned out that this property was insufficient to distinguish the given knot from a circle. Mr Malcolm next explained how group theory gave a characterisation which was sufficient for this but which becomes complicated and the subject has not yet been satisfactorily resolved by mathematicians.

—G.N.